


Paper's Title:
Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and realvalued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Paper's Title:
Credibility Based Fuzzy Entropy Measure
Author(s):
G. Yari, M. Rahimi, B. Moomivand and P. Kumar
Department of Mathematics,
Iran University
of Science and Technology,
Tehran,
Iran.
Email:
Yari@iust.ac.ir
Email:
Mt_Rahimi@iust.ac.ir
URL:
http://www.iust.ac.ir/find.php?item=30.11101.20484.en
URL:
http://webpages.iust.ac.ir/mt_rahimi/en.html
Qarzolhasaneh
Mehr Iran Bank, Tehran,
Iran.
Email:
B.moomivand@qmb.ir
Department of Mathematics and Statistics,
University of Northern British Columbia,
Prince George, BC,
Canada.
Email:
Pranesh.Kumar@unbc.ca
Abstract:
Fuzzy entropy is the entropy of a fuzzy variable, loosely representing the information of uncertainty. This paper, first examines both previous membership and credibility based entropy measures in fuzzy environment, and then suggests an extended credibility based measure which satisfies mostly in Du Luca and Termini axioms. Furthermore, using credibility and the proposed measure, the relative entropy is defined to measure uncertainty between fuzzy numbers. Finally we provide some properties of this Credibility based fuzzy entropy measure and to clarify, give some examples.
Paper's Title:
Iterative Approximation of Common Fixed Points of a Finite Family of Asymptotically Hemicontractive Type Mappings
Author(s):
JuiChi Huang
Center for General Education,
Northern Taiwan Institute of Science and Technology,
Peito, Taipei,
Taiwan, 11202, R.O.C.
juichi@ntist.edu.tw
Abstract:
In this paper, we prove that the sequence of
the modified IshikawaXu,
IshikawaLiu, MannXu and MannLiu iterative types of a finite family of
asymptotically hemicontractive type mappings converges strongly to a common
fixed point of the family in a real puniformly convex Banach space with
p>1. Our results improve and extend some recent results.
Paper's Title:
Ostrowski Type Fractional Integral Inequalities for Generalized (s,m,φ)preinvex Functions
Author(s):
Artion Kashuri and Rozana Liko
University of Vlora "Ismail Qemali",
Faculty of Technical Science,
Department of Mathematics, 9400,
Albania.
Email:
artionkashuri@gmail.com
Email: rozanaliko86@gmail.com
Abstract:
In the present paper, the notion of generalized (s,m,φ)preinvex function is introduced and some new integral inequalities for the left hand side of GaussJacobi type quadrature formula involving generalized (s,m,φ)preinvex functions along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for generalized (s,m,φ)preinvex functions via RiemannLiouville fractional integrals are established.
Paper's Title:
Generalized Weighted Trapezoid and Grüss Type Inequalities on Time Scales
Author(s):
Eze Raymond Nwaeze
Department of Mathematics,
Tuskegee University,
Tuskegee, AL 36088,
USA.
Email: enwaeze@mytu.tuskegee.edu
Abstract:
In this work, we obtain some new generalized weighted trapezoid and Grüss type inequalities on time scales for parameter functions. Our results give a broader generalization of the results due to Pachpatte in [14]. In addition, the continuous and discrete cases are also considered from which, other results are obtained.
Paper's Title:
Komatu Integral Transforms of Analytic Functions Subordinate to Convex Functions
Author(s):
T. N. Shanmugam and C. Ramachandran
Department of Mathematics, College of Engineering,
Anna University, Chennai600 025, Tamilnadu,
India
shan@annauniv.edu
Department of Mathematics, College of Engineering,
Anna University, Chennai600 025, Tamilnadu,
India
crjsp2004@yahoo.com
Abstract:
In this paper, we consider the class A of the functions f(z) of the form
which are analytic in an open disk
and study certain subclass of the class A, for which
has some property. Certain inclusion and the closure properties like convolution with convex univalent function etc. are studied.
Paper's Title:
A Subclass of Meromorphically Multivalent Functions with Applications to Generalized Hypergeometric Functions
Author(s):
M. K. Aouf
Mathematics Department,
Faculty of Science,
Mansoura University 35516,
Egypt
mkaouf127@yahoo.com
Abstract:
In this paper a new subclass of meromorphically multivalent functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically pvalent functions. The main object of the present paper is to investigate the various important properties and characteristics of this subclass of meromorphically multivalent functions. We also derive many interesting results for the Hadamard products of functions belonging to this subclass. Also we consider several applications of our main results to generalized hypergeomtric functions.
Paper's Title:
A Selfadaptive Subgradient Extragradient Algorithm for Variational Inequality Problems and Fixed Point Problems in Banach Spaces
Author(s):
F. U. Ogbuisi
School of Mathematics, Statistics and
Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Department of Mathematics,
University of Nigeria, Nsukka,
Nigeria.
Email: ferdinard.ogbuisi@unn.edu.ng
fudochukwu@yahoo.com
Abstract:
In this paper, we propose and analyze a type of subgradient extragradient algorithm for the approximation of a solution of variational inequality problem which is also a common fixed point of an infinite family of relatively nonexpansive mappings in 2uniformly convex Banach spaces which are uniformly smooth. By using the generalized projection operator, we prove a strong convergence theorem which does not require the prior knowledge of the Lipschitz constant of cost operator. We further applied our result to constrained convex minimization problem, convex feasibility problem and infinite family of equilibrium problems. Our results improve and complement related results in 2uniformly convex and uniformly smooth Banach spaces and Hilbert spaces.
Paper's Title:
Fractional exp(φ(ξ)) Expansion Method and its Application to SpaceTime Nonlinear Fractional Equations
Author(s):
A. A. Moussa and L. A. Alhakim
Department of Management Information
System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
Email: Alaamath81@gmail.com
URL:
https://scholar.google.com/citations?user=ccztZdsAAAAJ&hl=ar
Department of Management Information
System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
Email: Lama2736@gmail.com
URL:
https://scholar.google.com/citations?user=OSiSh1AAAAAJ&hl=ar
Abstract:
In this paper, we mainly suggest a new method that depends on the fractional derivative proposed by Katugampola for solving nonlinear fractional partial differential equations. Using this method, we obtained numerous useful and surprising solutions for the spacetime fractional nonlinear WhithamBroerKaup equations and spacetime fractional generalized nonlinear HirotaSatsuma coupled KdV equations. The solutions obtained varied between hyperbolic, trigonometric, and rational functions, and we hope those interested in the reallife applications of the previous two equations will find this approach useful.
Paper's Title:
Local and Global Existence and Uniqueness Results for Second and Higher Order Impulsive Functional Differential Equations with Infinite Delay
Author(s):
Johnny Henderson and Abdelghani Ouahab
Department of Mathematics, Baylor University,
Waco, Texas 767987328
USA.
Johnny_Henderson@baylor.edu
Laboratoire de Mathématiques, Université de Sidi Bel Abbés
BP 89, 22000 Sidi Bel Abbées,
Algérie.
ouahab@univsba.dz
Abstract:
In this paper, we discuss the local and global existence and uniqueness results for second and higher order impulsive functional differential equations with infinite delay. We shall rely on a nonlinear alternative of LeraySchauder. For the global existence and uniqueness we apply a recent Frigon and Granas nonlinear alternative of LeraySchauder type in Fréchet spaces.
Paper's Title:
Long Correlations Applied to the Study of Agricultural Indices in Comparison with the S&P500 index
Author(s):
M. C. Mariani, J. Libbin, M.P. Beccar Varela,
V. Kumar Mani, C. Erickson, D.J. Valles Rosales
Department of Mathematical Sciences,
Science Hall 236, New Mexico State University,
Las Cruces, NM 880038001,
USA.
mmariani@nmsu.edu
Abstract:
Longtime correlations in agricultural indices are studied and their behavior is compared to the wellestablished S&P500 index. Hurst exponent and Detrended Fluctuation Analysis (DFA) techniques are used in this analysis. We detected longcorrelations in the agricultural indices and briefly discussed some features specific in comparison to the S&P500 index.
Paper's Title:
Approximation of Common Fixed Points of a Finite Family of Asymptotically Demicontractive Mappings in Banach Spaces
Author(s):
Yuchao Tang,^{ }Yong Cai, Liqun Hu and Liwei Liu
Department of Mathematics, NanChang University,
Nanchang 330031, P.R. China
Department of Mathematics, Xi'an Jiaotong University,
Xi'an 710049, P.R.
China
Abstract:
By virtue of new analytic techniques, we analyze and
study
several strong convergence theorems for the approximation of
common fixed points of asymptotically demicontractive mappings
via the multistep iterative sequence with errors in Banach
spaces. Our results improve and extend the corresponding ones
announced by Osilike , Osilike and Aniagbosor, Igbokwe, Cho et
al., Moore and Nnoli, Hu and all the others.
Paper's Title:
On Convergence Theorems of an Implicit Iterative Process with Errors for a Finite Family of Asymptotically quasi Inonexpansive Mappings
Author(s):
Farrukh Mukhamedov and Mansoor Saburov
Department of Computational & Theoretical
Sciences,
Faculty of Sciences, International Islamic University Malaysia,
P.O. Box, 141, 25710, Kuantan,
Malaysia
Abstract:
In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family {T_{j}}^{N}_{i=1} of asymptotically quasi I_{j}nonexpansive mappings as well as a family of {Ij}^{N}_{j=1} of asymptotically quasi nonexpansive mappings in the framework of Banach spaces. The obtained results improve and generalize the corresponding results in the existing literature.
Paper's Title:
Two Geometric Constants Related to Isosceles Orthogonality on Banach Space
Author(s):
Huayou Xie, Qi Liu and Yongjin Li
Department of Mathematics,
Sun Yatsen University,
Guangzhou, 510275,
P. R. China.
Email: xiehy33@mail2.sysu.edu.cn
Department of Mathematics,
Sun Yatsen University,
Guangzhou, 510275,
P. R. China.
Email: liuq325@mail2.sysu.edu.cn
Department of Mathematics,
Sun Yatsen University,
Guangzhou, 510275,
P. R. China.
Email: stslyj@mail.sysu.edu.cn
Abstract:
In this paper, we introduce new geometric constant C(X,a_{i},b_{i},c_{i},2) to measure the difference between isosceles orthogonality and special Carlsson orthogonalities. At the same time, we also present the geometric constant C(X,a_{i},b_{i},c_{i}), which is a generalization of the rectangular constant proposed by Joly. According to the inequality on isosceles orthogonality, we give the boundary characterization of these geometric constants. Then the relationship between these geometric constants and uniformly nonsquare property can also be discussed. Furthermore, we show that there is a close relationship between these geometric constants and some important geometric constants.
Paper's Title:
Uniqueness Problems for Difference Polynomials Sharing a NonZero Polynomial of Certain Degree With Finite Weight
Author(s):
V. Priyanka, S. Rajeshwari and V. Husna
Department of Mathematics,
School of Engineering,
Presidency University,
Bangalore560064,
India.
Email:
priyapriyankaram1994@gmail.com
rajeshwaripreetham@gmail.com
husnav43@gmail.com
Abstract:
In this paper, we prove a result on the value distribution of difference polynomials sharing higher order derivatives of meromorphic functions which improves some earlier results. At the same time, we also prove possible uniqueness relation of entire functions when the difference polynomial generated by them sharing a non zero polynomial of certain degree. The result obtained in the paper will improve and generalize a number of recent results in a compact and convenient way.
Paper's Title:
A general theory of decision making
Author(s):
Frank Hansen
Department of Economics,
University of Copenhagen,
Studiestraede 6, DK1455 Copenhagen K
Denmark
Frank.Hansen@econ.ku.dk
URL: http://www.econ.ku.dk/okofh
Abstract:
We formulate a general theory of decision making based on a lattice of observable events, and we exhibit a large class of representations called the general model. Some of the representations are equivalent to the so called standard model in which observable events are modelled by an algebra of measurable subsets of a state space, while others are not compatible with such a description. We show that the general model collapses to the standard model, if and only if an additional axiom is satisfied. We argue that this axiom is not very natural and thus assert that the standard model may not be general enough to model all relevant phenomena in economics. Using the general model we are (as opposed to Schmeidler [16]) able to rationalize Ellsberg's paradox without the introduction of nonadditive measures.
Paper's Title:
Inclusion Properties of a Certain Subclass of Strongly CloseToConvex Functions
Author(s):
S. M. Khairnar and M. More
Department of Mathematics,
Maharashtra Academy of Engineerring,
Alandi 412 105, Pune, Maharashtra,
INDIA.
smkhairnar2007@gmail.com,
meenamores@gmail.com.
Abstract:
The purpose of this paper is to derive some inclusion and argument properties of a new subclass of strongly closetoconvex functions in the open unit disc. We have considered an integral operator defined by convolution involving hypergeometric function in the subclass definition. The subclass also extends to the class of αspirallike functions of complex order.
Paper's Title:
A Geometric Generalization of BusemannPetty Problem
Author(s):
Liu Rong and Yuan Jun
Shanghai Zhangjiang Group Junior Middle School,
Huo Xiang Road, Shanghai, 201203,
China
Abstract:
The norm defined by Busemann's inequality establishes a class of star body  intersection body. This class of star body plays a key role in the solution of BusemannPetty problem. In 2003, Giannapoulos [1] defined a norm for a new class of halfsection. Based on this norm, we give a geometric generalization of BusemannPetty problem, and get its answer as a result
Paper's Title:
Strong Convergence Theorem for a Common Fixed Point of an Infinite Family of Jnonexpansive Maps with Applications
Author(s):
Charlse Ejike Chidume, Otubo Emmanuel Ezzaka and Chinedu Godwin Ezea
African University of Science and
Technology,
Abuja,
Nigeria.
Email:
cchidume@aust.edu.ng
Ebonyi State University,
Abakaliki,
Nigeria.
Email: mrzzaka@yahoo.com
Nnamdi Azikiwe University,
Awka,
Nigeria.
Email: chinedu.ezea@gmail.com
Abstract:
Let E be a uniformly convex and uniformly smooth real Banach space with dual space E^{*}. Let {T_{i}}^{∞}_{i=1} be a family of Jnonexpansive maps, where, for each i,~T_{i} maps E to 2^{E*}. A new class of maps, Jnonexpansive maps from E to E^{*}, an analogue of nonexpansive self maps of E, is introduced. Assuming that the set of common Jfixed points of {T_{i}}^{∞}_{i=1} is nonempty, an iterative scheme is constructed and proved to converge strongly to a point x^{*} in ∩^{∞}_{n=1}F_{J}T_{i}. This result is then applied, in the case that E is a real Hilbert space to obtain a strong convergence theorem for approximation of a common fixed point for an infinite family of nonexpansive maps, assuming existences. The theorem obtained is compared with some important results in the literature. Finally, the technique of proof is also of independent interest.
Paper's Title:
An Integration Technique for Evaluating Quadratic Harmonic Sums
Author(s):
J. M. Campbell and K.W. Chen
Department of Mathematics and Statistics,
York University, 4700 Keele St, Toronto,
ON M3J 1P3,
Canada.
Email: jmaxwellcampbell@gmail.com
Department of Mathematics, University of Taipei,
No. 1, AiGuo West Road,
Taipei 10048, Taiwan.
Email: kwchen@uTaipei.edu.tw
URL:
https://math.utaipei.edu.tw/p/412108222.php
Abstract:
The modified Abel lemma on summation by parts has been applied in many ways recently to determine closedform evaluations for infinite series involving generalized harmonic numbers with an upper parameter of two. We build upon such results using an integration technique that we apply to ``convert'' a given evaluation for such a series into an evaluation for a corresponding series involving squared harmonic numbers.
Paper's Title:
Fixed Point Theorems for a Finite Family of Asymptotically Nonexpansive Mappings
Author(s):
E. Prempeh
Department of Mathematics,
Kwame Nkrumah University of Science and Technology,
Kumasi, Ghana
edward_prempeh2000@yahoo.com
Abstract:
Let _{} be a real reflexive Banach space with a uniformly Gâteaux differentiable norm, _{} be a nonempty bounded closed convex subset of _{} i=1,2,...,r be a finite family of asymptotically nonexpansive mappings such that for each _{} Let _{ } be a nonempty set of common fixed points of _{} and define
_{} . Let _{} be fixed and let _{} be such that _{} as _{} . We can prove that the sequence _{} satisfying the relation_{} associated with _{} , converges strongly to a fixed point of _{} provided _{} possesses uniform normal structure. Furthermore we prove that the iterative process: _{} _{}
_{} , converges strongly to a fixed point of _{}
Paper's Title:
The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations
Author(s):
Alexandru Mihai Bica
Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro
Abstract:
We present here a numerical method for first order delay ordinary differential equations, which use the Banach's fixed point theorem, the sequence of successive approximations and the trapezoidal quadrature rule. The error estimation of the method uses a recent result of P. Cerone and S.S. Dragomir about the remainder of the trapezoidal quadrature rule for Lipchitzian functions and for functions with continuous first derivative.
Paper's Title:
Boundedness for VectorValued Multilinear Singular Integral Operators on TriebelLizorkin Spaces
Author(s):
Liu Lanzhe
College of Mathematics
Changsha University of Science and Technology,
Changsha 410077,
P.R. of China.
lanzheliu@263.net
Abstract:
In this paper, the boundedness for some vectorvalued multilinear operators associated to certain fractional singular integral operators on TriebelLizorkin space are obtained. The operators include CalderónZygmund singular integral operator and fractional integral operator.
Paper's Title:
Normalized Truncated Levy models applied to the study of Financial Markets
Author(s):
M. C. Mariani, K. Martin, D. W. Dombrowski and D. Martinez
Department of Mathematical Sciences and Department of Finance,
New Mexico State University, P.O. Box 30001
Department 3MB Las Cruces, New Mexico 880038001
USA.
mmariani@nmsu.edu
kjmartin@nmsu.edu
Abstract:
This work is devoted to the study of the statistical properties of financial instruments from developed markets. We performed a new analysis of the behavior of companies corresponding to the DJIA index, and of the index itself, by using a normalized Truncated Levy walk model. We conclude that the Truncated Levy distribution describes perfectly the evolution of the companies and of the index near a crash.
Paper's Title:
On a Subclass of Uniformly Convex Functions Defined by the DziokSrivastava Operator
Author(s):
M. K. Aouf and G. Murugusundaramoorthy
Mathematics Department, Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com
School of Science and Humanities, VIT University
Vellore  632014,
India.
gmsmoorthy@yahoo.com
Abstract:
Making use of the DziokSrivastava operator, we define a new subclass T^{l}_{m}([α_{1}];α,β) of uniformly convex function with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorems, locate extreme points and obtain radii of closetoconvexity, starlikeness and convexity for functions belonging to the class T^{l}_{m}([α_{1}];α,β) . We consider integral operators associated with functions belonging to the class H^{l}_{m}([α_{1}];α,β) defined via the DziokSrivastava operator. We also obtain several results for the modified Hadamard products of functions belonging to the class T^{l}_{m}([α_{1}];α,β) and we obtain properties associated with generalized fractional calculus operators.
Paper's Title:
On the Three Variable Reciprocity Theorem and Its Applications
Author(s):
D. D. Somashekara and D. Mamta
Department of Studies in Mathematics,
University of Mysore,
Manasagangotri, Mysore570 006
India
dsomashekara@yahoo.com
Department of Mathematics,
The National Institute of Engineering,
Mysore570 008,
India
mathsmamta@yahoo.com
Abstract:
In this paper we show how the three variable reciprocity theorem can be easily derived from the well known two variable reciprocity theorem of Ramanujan by parameter augmentation. Further we derive some qgamma, qbeta and etafunction identities from the three variable reciprocity theorem.
Paper's Title:
On A Conjecture of A Logarithmically Completely Monotonic Function
Author(s):
Valmir Krasniqi, Armend Sh. Shabani
Department of Mathematics,
University of Prishtina,
Republic of Kosova
Email:
vali.99@hotmail.com
armend_shabani@hotmail.com
Abstract:
In this short note we prove a conjecture, related to a logarithmically completely monotonic function, presented in [5]. Then, we extend by proving a more generalized theorem. At the end we pose an open problem on a logarithmically completely monotonic function involving qDigamma function.
Paper's Title:
Strong Convergence Theorems for a Common Zero of an Infinite Family of GammaInverse Strongly Monotone Maps with Applications
Author(s):
Charles Ejike Chidume, Ogonnaya Michael Romanus, and Ukamaka Victoria Nnyaba
African University of Science and
Technology, Abuja,
Nigeria.
Email: cchidume@aust.edu.ng
Email: romanusogonnaya@gmail.com
Email: nnyabavictoriau@gmail.com
Abstract:
Let E be a uniformly convex and uniformly smooth real Banach space with
dual space E^{*} and let A_{k}:E→E^{*},
k=1, 2, 3 , ...
be a family of inverse strongly monotone maps such that ∩^{∞}_{k=1}
A_{k}^{1}(0)≠∅.
A new iterative algorithm is constructed and proved to converge strongly to a
common zero of the family.
As a consequence of this result, a strong convergence theorem for approximating
a common Jfixed point for an infinite family of
gammastrictly Jpseudocontractive maps is proved. These results are new and
improve recent results obtained for these classes of nonlinear maps.
Furthermore, the technique of proof is of independent interest.
Paper's Title:
A Generalization of Ostrowski's Inequality for Functions of Bounded Variation via a Parameter
Author(s):
Seth Kermausuor
Department of Mathematics and Computer
Science,
Alabama State University,
Montgomery, AL 36101,
USA.
Email:
skermausour@alasu.edu
Abstract:
In this paper, we provide a generalization of the Ostrowski's inequality for functions of bounded variation for k points via a parameter λ∈[0,1]. As a by product, we consider some particular cases to obtained some interesting inequalities in these directions. Our results generalizes some of the results by Dragomir in [S. S. DRAGOMIR, The Ostrowski inequality for mappings of bounded variation, Bull. Austral. Math. Soc., 60 (1999), pp. 495508.]
Paper's Title:
Inequalities for Functions of Selfadjoint Operators on Hilbert Spaces:
a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics,
College of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
https://rgmia.org/dragomir
Abstract:
The main aim of this survey is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Paper's Title:
RiemannStieltjes Integrals and Some Ostrowski Type Inequalities
Author(s):
W. G. Alshanti
Department of General Studies,
Jubail University College,
KSA.
Email: shantiw@ucj.edu.sa
Abstract:
In this article, we investigate new integral inequalities of Ostrowski's type of various functional aspects. For mapping's second derivative, we assume two cases, namely, L_{1} and L_{∞} spaces. Moreover, for first derivative, we investigate two different characteristics, namely, bounded variation and locally Lipchitz continuity. Applications to special means and composite quadrature rules are also carried out.
Paper's Title:
Trace Inequalities for Operators in Hilbert Spaces: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics,
School of Engineering
& Science
Victoria University,
PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
https://rgmia.org/dragomir
Abstract:
In this paper we survey some recent trace inequalities for operators in Hilbert spaces that are connected to Schwarz's, Buzano's and Kato's inequalities and the reverses of Schwarz inequality known in the literature as Cassels' inequality and ShishaMond's inequality. Applications for some functionals that are naturally associated to some of these inequalities and for functions of operators defined by power series are given. Further, various trace inequalities for convex functions are presented including refinements of Jensen inequality and several reverses of Jensen's inequality. HermiteHadamard type inequalities and the trace version of Slater's inequality are given. Some Lipschitz type inequalities are also surveyed. Examples for fundamental functions such as the power, logarithmic, resolvent and exponential functions are provided as well.
Paper's Title:
SQIRV Model for Omicron Variant with Time Delay
Author(s):
S. Dickson, S. Padmasekaran, G. E. Chatzarakis and S. L. Panetsos
Mathematics, Periyar University, Periyar
Palkalai Nagar, Salem,
636011, Tamilnadu,
India.
Email:
dickson@periyaruniversity.ac.in,
padmasekarans@periyaruniversity.ac.in
Electrical and Electronic Engineering
Educators, School of
Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
Email: geaxatz@otenet.gr,
spanetsos@aspete.gr
Abstract:
In order to examine the dynamics of the Omicron variant, this paper uses mathematical modelling and analysis of a SQIRV model, taking into account the delay in the conversion of susceptible individuals into infected individuals and infected individuals into recovered individuals. The pandemic was eventually controlled as a result of the massive delays. To assure the safety of the host population, this concept incorporates quarantine and the COVID19 vaccine. Both local and global stability of the model are examined. It is found that the fundamental reproduction number affects both local and global stability conditions. Our findings show that asymptomatic cases caused by an affected population play an important role in increasing Omicron infection in the general population. The most recent data on the pandemic Omicron variant from Tamil Nadu, India, is verified.
Paper's Title:
A Self Adaptive Method for Solving Split Bilevel Variational Inequalities Problem in Hilbert Spaces
Author(s):
Francis Akutsah^{1}, Ojen Kumar Narain^{2}, Funmilayo Abibat Kasali^{3} Olawale Kazeem Oyewole^{4} and Akindele Adebayo Mebawondu^{5}
^{1}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: 216040405@stu.ukzn.ac.za,
akutsah@gmail.com
^{2}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: naraino@ukzn.ac.za
^{3}Mountain Top University,
Prayer City, Ogun State,
Nigeria.
Email: fkasali@mtu.edu.ng
^{4}TechnionIsrael
Institute of Technology.
Email: 217079141@stu.ukzn.ac.za,
oyewoleolawalekazeem@gmail.co
^{5}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
DSTNRF Centre of Excellence in Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Mountain Top University,
Prayer City, Ogun State,
Nigeria.
Email: dele@aims.ac.za
Abstract:
In this work, we study the split bilevel variational inequality problem in two real Hilbert spaces. We propose a new modified inertial projection and contraction method for solving the aforementioned problem when one of the operators is pseudomonotone and Lipschitz continuous while the other operator is αstrongly monotone. The use of the weakly sequential continuity condition on the Pseudomonotone operator is removed in this work. A Strong convergence theorem of the proposed method is proved under some mild conditions. In addition, some numerical experiments are presented to show the efficiency and implementation of our method in comparison with other methods in the literature in the framework of infinite dimensional Hilbert spaces. The results obtained in this paper extend, generalize and improve several.
Paper's Title:
Higher Order Accurate Compact Schemes for Time Dependent Linear and Nonlinear ConvectionDiffusion Equations
Author(s):
S. Thomas, Gopika P.B. and S. K. Nadupuri
Department of Mathematics
National Institute of Technology Calicut
Kerala
673601
India.
Email:
sobinputhiyaveettil@gmail.com
pbgopika@gmail.com nsk@nitc.ac.in
Abstract:
The primary objective of this work is to study higher order compact finite difference schemes for finding the numerical solution of convectiondiffusion equations which are widely used in engineering applications. The first part of this work is concerned with a higher order exponential scheme for solving unsteady one dimensional linear convectiondiffusion equation. The scheme is set up with a fourth order compact exponential discretization for space and cubic $C^1$spline collocation method for time. The scheme achieves fourth order accuracy in both temporal and spatial variables and is proved to be unconditionally stable. The second part explores the utility of a sixth order compact finite difference scheme in space and Huta's improved sixth order RungeKutta scheme in time combined to find the numerical solution of one dimensional nonlinear convectiondiffusion equations. Numerical experiments are carried out with Burgers' equation to demonstrate the accuracy of the new scheme which is sixth order in both space and time. Also a sixth order in space predictorcorrector method is proposed. A comparative study is performed of the proposed schemes with existing predictorcorrector method. The investigation of computational order of convergence is presented.
Paper's Title:
Jordan Canonical Form of Interval Matrices and Applications
Author(s):
S. Hema Surya, T. Nirmala and K. Ganesan
Department of Mathematics, College of
Engineering and Technology,
SRM Institute of Science and Technology,
Kattankulathur,
Chennai603203,
India.
Email: nirmalat@srmist.edu.in
URL:
https://www.srmist.edu.in/faculty/drtnirmala/
Abstract:
A square interval matrix over R can be converted to diagonal form if certain prerequisites are satisfied. However not all square matrices can be diagonalized. As a consequence, we strive the next simplest form to which it can be reduced while retaining important properties such as eigenvalues, rank, nullity, and so on. It turns out that any real interval matrix has a Jordan Canonical Form (JCF) over E if it has n interval eigenvalues in IR. We discuss in this paper a method for computing the Jordan canonical form of an interval matrix using a new pairing technique and a new type of interval arithmetic that will make classifying and analyzing interval matrices easier and more efficient. We conclude with a numerical example that supports the theory and application of predatorprey model.
Paper's Title:
A General Fractional Control Scheme for Compound Combination Synchronization Between Different FractionalOrder Identical Chaotic Systems
Author(s):
Soumia Bensimessaoud and Smail Kaouache
Laboratory of Mathematics and their interactions, Abdelhafid Boussouf University Center, Mila, Algeria.
Email:
soumiabensimessaoud@gmail.com,
smailkaouache@gmail.com
Abstract:
In this paper, we aim to investigate the problem of compound combination synchronization (CCS) between four different fractionalorder identical chaotic systems. Based on Laplace transformation and stability theory of linear dynamical systems, a new control law is proposed to assure the achievement of this kind of synchronization. Secondly, this control scheme is applied to realised CCS between four identical unified chaotic systems. Recall, that the proposed control scheme can be applied to wide classes of chaotic and hyperchaotic systems. Numerical simulations are given to show the effectiveness of the proposed method.
Paper's Title:
Mass Transportation Approach For Parabolic PBiharmonic Equations
Author(s):
A. Soglo, K. W. Houedanou, J. Adetola
Institut de Mathematiques et de Sciences
Physiques (IMSP)
Universite d'AbomeyCalavi,
Rep. of Benin
Email: ambroiso.soglo@gmail.com
Departement de Mathematiques
Faculte des Sciences et Techniques (FAST)
Universite d'AbomeyCalavi,
Rep. of Benin
Email: khouedanou@yahoo.fr
Universite Nationale des Sciences, Technologie, Ingenierie et
Mathematiques (UNSTIM,
Abomey,
Rep. of Benin
Email: adetolajamal58@yahoo.com
Abstract:
In this paper, we propose a mass transportation method to solving a parabolic pbiharmonic equations, which generalized the CahnHilliard (CH) equations in R^{N}, N∈N^{*}. By using a timestep optimal approximation in the appropriate Wasserstein space, we define an approximate weak solution which converges to the exact solution of the problem. We also show that the solution under certain conditions may be unique. Therefore, we study the asymptotic behavior of the solution of the parabolic pbiharmonic problem.
Paper's Title:
Existence of solutions for Neutral Stochastic Functional Differential Systems with Infinite Delay in Abstract Space
Author(s):
P. Balasubramaniam, A. V. A. Kumar and S. K. Ntouyas
Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram  624 302,
Tamil Nadu, India.
pbalgri@rediffmail.com
Department of Mathematics, Gandhigram Rural Institute,
Deemed University, Gandhigram  624 302,
Tamil Nadu, India.
nnddww@tom.com
Department of Mathematics, University of Ioannina,
451 10 Ioannina,
Greece.
sntouyas@cc.uoi.gr
URL: http://www.math.uoi.gr/~sntouyas
Abstract:
In this paper we prove existence results for semilinear stochastic neutral functional differential systems with unbounded delay in abstract space. Our theory makes use of analytic semigroups and fractional power of closed operators and Sadovskii fixed point theorem.
Paper's Title:
Existence of Solutions for Third Order Nonlinear Boundary Value Problems
Author(s):
Yue Hu and Zuodong Yang
School of Mathematics and Computer Science, Nanjing Normal University, Jiangsu Nanjing 210097,
China.
huu3y2@163.com
College of Zhongbei, Nanjing Normal University, Jiangsu Nanjing 210046,
China.
zdyang_jin@263.net
yangzuodong@njnu.edu.cn
Abstract:
In this paper, the existence of solution for a class of third order quasilinear ordinary differential equations with nonlinear boundary value problems
(Φ_{p}(u"))'=f(t,u,u',u"), u(0)=A, u'(0)=B, R(u'(1),u"(1))=0
is established. The results are obtained by using upper and lower solution methods.
Paper's Title:
Positive Periodic Solutions for SecondOrder Differential Equations with Generalized Neutral Operator
Author(s):
WingSum Cheung, Jingli Ren and Weiwei Han
Department of Mathematics,
The University of Hong Kong
Pokfulam
Road,
Hong Kong
Department of Mathematics, Zhengzhou University
Zhengzhou 450001,
P.R. China
wscheung@hkucc.hku.hk
renjl@zzu.edu.cn
Abstract:
By some analysis of the neutral operator and an application of the fixedpoint index theorem, we obtain sufficient conditions for the existence, multiplicity and nonexistence of periodic solutions to a secondorder differential equation with the prescribed neutral operator, which improve and extend some recent results of LuGe, WuWang, and Zhang. An example is given to illustrate our results. Moreover, the analysis of the generalized neutral operator will be helpful for other types of differential equations.
Paper's Title:
Inequalities for the Čebyšev Functional of Two Functions of Selfadjoint Operators in Hilbert Spaces
Author(s):
S. S. Dragomir
School of Engineering and Science
Victoria University, PO 14428
Melbourne City MC,
Victoria 8001,
Australia
sever.dragomir@vu.edu.au
URL: http://www.staff.vu.edu.au/RGMIA/dragomir/
Abstract:
Some recent inequalities for the Čebyšev functional of two functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved functions and operators, are surveyed.
Paper's Title:
Applications of Relations and Relators in the Extensions of Stability Theorems for Homogeneous and Additive Functions
Author(s):
Árpád Száz
Institute of Mathematics, University of Debrecen,
H4010 Debrecen,
Pf. 12,
Hungary
szaz@math.klte.hu
Abstract:
By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.
Paper's Title:
A Coincidence Theorem for Two Kakutani Maps
Author(s):
Mircea Balaj
Department of Mathematics,
University of Oradea,
410087, Oradea,
Romania.
mbalaj@uoradea.ro
Abstract:
In this paper we prove the following theorem: Let X be a nonempty compact convex set in a locally convex Hausdorff topological vector space, D be the set of its extremal points and F,T: X―◦X two Kakutani maps; if for each nonempty finite subset A of D and for any x ∈ coA, F (x) ∩ coA ≠ Ř, then F and T have a coincidence point. The proof of this theorem is given first in the case when X is a simplex, then when X is a polytope and finally in the general case. Several reformulations of this result are given in the last part of the paper.
Paper's Title:
SEVERAL qINTEGRAL INEQUALITIES
Author(s):
W. T. Sulaiman
Department of Computer Engineering,
College of Engineering,
University of Mosul,
Iraq.
waadsulaiman@hotmail.com
Abstract:
In the present paper several qintegral inequalities are presented, some of them are new and others are generalizations of known results.
Paper's Title:
A Differential Sandwich Theorem for Analytic Functions Defined by the Generalized Sălăgean Operator
Author(s):
D. Răducanu and V. O. Nechita
Faculty of Mathematics and Computer
Science,
"Transilvania" University Braşov
Str. Iuliu Maniu 50, 500091 Braşov,
Romania
dorinaraducanu@yahoo.com
Faculty of Mathematics and Computer
Science,
"BabeşBolyai" University ClujNapoca,
Str. M. Kogalniceanu 1, 400084 ClujNapoca,
Romania
URL:
http://math.ubbcluj.ro/~vnechita/
vnechita@math.ubbcluj.ro
Abstract:
We obtain some subordination and superordination results involving the generalized Sălăgean differential operator for certain normalized analytic functions in the open unit disk. Our results extend corresponding previously known results.
Paper's Title:
On a Class of Meromorphic Functions of Janowski Type Related with a Convolution Operator
Author(s):
Abdul Rahman S. Juma, Husamaldin I. Dhayea
Department of
Mathematics,
Alanbar University, Ramadi,
Iraq.
Email: dr_juma@hotmail.com
Department of Mathematics,
Tikrit University, Tikrit,
Iraq.
URL: husamaddin@gmail.com
Abstract:
In this paper, we have introduced and studied new operator $Q^{k}_{λ,m,γ} by the Hadamard product (or convolution) of two linear operators D^{k}_{λ} and I_{m,γ}, then using this operator to study and investigate a new subclass of meromorphic functions of Janowski type, giving the coefficient bounds, a sufficient condition for a function to belong to the considered class and also a convolution property. The results presented provide generalizations of results given in earlier works.
Paper's Title:
Existence of Positive Solutions for Nonlinear Fractional Differential Equations with Multipoint Boundary Conditions
Author(s):
N. Adjeroud
Khenchela University, Department of
Mathematics,
Khenchela, 40000,
Algeria.
Email: adjnac@gmail.com
Abstract:
This paper is devoted to the existence results of positive solutions for a nonlinear fractional differential equations with multipoint boundary conditions. By means of the Schauder fixed point theorem, some results on the existence are obtained.
Paper's Title:
Convergence Speed of Some Random ImplicitKirktype Iterations for Contractivetype Random Operators
Author(s):
H. Akewe, K.S. Eke
Department of Mathematics,
Covenant University,
Canaanland, KM 10, Idiroko Road, P. M. B. 1023, Ota, Ogun State,
Nigeria.
Email: hudson.akewe@covenantuniversity.edu.ng,
kanayo.eke@covenantuniversity.edu.ng
Abstract:
The main aim of this paper is to introduce a stochastic version of multistep type iterative scheme called a modified random implicitKirk multistep iterative scheme and prove strong convergence and stability results for a class of generalized contractivetype random operators. The rate of convergence of the random iterative schemes are also examined through an example. The results show that our new random implicit kirk multistep scheme perform better than other implicit iterative schemes in terms of convergence and thus have good potentials for further applications in equilibrium problems in computer science, physics and economics.
Paper's Title:
Existence and Estimate of the Solution for the Approximate Stochastic Equation to the Viscous Barotropic Gas
Author(s):
R. Benseghir and A. Benchettah
LANOS Laboratory,
Badji Mokhtar University,
PO Box 12,
Annaba, Algeria.
Email:
benseghirrym@ymail.com,
abenchettah@hotmail.com
Abstract:
A stochastic equation of a viscous barotropic gas is considered. The application of Ito formula to a specific functional in an infinite dimensional space allows us to obtain an estimate which is useful to analyse the behavior of the solution. As it is difficult to exploit this estimate, we study an approximate problem. More precisely, we consider the equation of a barotropic viscous gas in Lagrangian coordinates and we add a diffusion of the density. An estimate of energy is obtained to analyse the behavior of the solution for this approximate problem and Galerkin method is used to prove the existence and uniqueness of the solution.
Paper's Title:
An Existence of the Solution to Neutral Stochastic Functional Differential Equations Under the Holder Condition
Author(s):
YoungHo Kim
Department of Mathematics,
Changwon National University,
Changwon, Gyeongsangnamdo 51140,
Korea.
Email: iyhkim@changwon.ac.kr
Abstract:
In this paper, we show the existence and uniqueness of solution of the neutral stochastic functional differential equations under weakened H\"{o}lder condition, a weakened linear growth condition, and a contractive condition. Furthermore, in order to obtain the existence of a solution to the equation we used the Picard sequence.
Paper's Title:
Some New Mappings Related to Weighted Mean Inequalities
Author(s):
XiuFen Ma
College of Mathematical and Computer,
Chongqing Normal University Foreign Trade and Business College,
No.9 of Xuefu Road, Hechuan District 401520,
Chongqing City,
The People's Republic of China.
Email: maxiufen86@163.com
Abstract:
In this paper, we define four mappings related to weighted mean inequalities, investigate their properties, and obtain some new refinements of weighted mean inequalities.
Paper's Title:
Several Applications of a Local Nonconvex Youngtype Inequality
Author(s):
Loredana Ciurdariu, Sorin Lugojan
Department of Mathematics,
"Politehnica" University of Timisoara,
Pta. Victoriei, No.2, 300006Timisoara,
Romania.
Email: ltirtirau87@yahoo.com
Abstract:
A local version of the Young inequality for positive numbers is used in order to deduce some inequalities about determinants and norms for real quadratic matrices and norms of positive operators on complex Hilbert spaces.
Paper's Title:
On Ruled Surfaces According to QuasiFrame in Euclidean 3Space
Author(s):
M. Khalifa Saad and R. A. AbdelBaky
Department of Mathematics, Faculty of
Science,
Islamic University of Madinah,
KSA.
Department of Mathematics, Faculty of Science,
Sohag University, Sohag,
EGYPT.
Email:
mohamed_khalifa77@science.sohag.edu.eg,
mohammed.khalifa@iu.edu.sa
Department of Mathematics, Faculty of
Science,
Assiut University, Assiut,
EGYPT.
Email: rbaky@live.com
Abstract:
This paper aims to study the skew ruled surfaces by using the quasiframe of Smarandache curves in the Euclidean 3space. Also, we reveal the relationship between SerretFrenet and quasiframes and give a parametric representation of a directional ruled surface using the quasiframe. Besides, some comparative examples are given and plotted which support our method and main results.
Paper's Title:
Double Difference of Composition Operator on Bloch Spaces
Author(s):
Rinchen Tundup
Department of Mathematics
University of Jammu
Jammu and Kashmir
India.
Email: joneytun123@gmail.com
Abstract:
In this paper we characterize the compactness of double difference of three noncompact composition operators on Bloch space induced by three holomorphic self maps on the unit disc.
Paper's Title:
Reduced Generalized Combination Synchronization Between Two nDimensional IntegerOrder Hyperchaotic Systems and One mDimensional FractionalOrder Chaotic System
Author(s):
Smail Kaouache, Mohammed Salah Abdelouahab and Rabah Bououden
Laboratory of Mathematics and their
interactions,
Abdelhafid Boussouf University Center, Mila.
Algeria
Email: smailkaouache@gmail.com,
medsalah3@yahoo.fr,
rabouden@yahoo.fr
Abstract:
This paper is devoted to investigate the problem of reduced generalized combination synchronization (RGCS) between two ndimensional integerorder hyperchaotic drive systems and one mdimensional fractionalorder chaotic response system. According to the stability theorem of fractionalorder linear system, an active mode controller is proposed to accomplish this end. Moreover, the proposed synchronization scheme is applied to synchronize three different chaotic systems, which are the Danca hyperchaotic system, the modified hyperchaotic Rossler system, and the fractionalorder RabinovichFabrikant chaotic system. Finally, numerical results are presented to fit our theoretical analysis.
Paper's Title:
Sweeping Surfaces with Darboux Frame in Euclidean 3space E3
Author(s):
F. Mofarreh, R. AbdelBaky and N. Alluhaibi
Mathematical Science Department, Faculty
of Science,
Princess Nourah bint Abdulrahman University
Riyadh 11546,
Saudi Arabia.
Email: fyalmofarrah@pnu.edu.sa
Department of Mathematics, Faculty of Science,
University of Assiut,
Assiut 71516,
Egypt.
Email: rbaky@live.com
Department of Mathematics Science and
Arts, College Rabigh Campus,
King Abdulaziz University
Jeddah,
Saudi Arabia.
Email: nallehaibi@kau.edu.sa
Abstract:
The curve on a regular surface has a moving frame and it is called Darboux frame. We introduce sweeping surfaces along the curve relating to the this frame and investigate their geometrical properties. Moreover, we obtain the necessary and sufficient conditions for these surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced.
Paper's Title:
A New Method with Regularization for Solving Split Variational Inequality Problems in Real Hilbert Spaces
Author(s):
Francis Akutsah^{1} and Ojen Kumar Narain^{2}
^{1}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: 216040405@stu.ukzn.ac.za,
akutsah@gmail.com
^{2}School
of Mathematics,
Statistics and Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: naraino@ukzn.ac.za
Abstract:
In this paper, we introduce a new inertial extrapolation method with regularization for approximating solutions of split variational inequality problems in the frame work of real Hilbert spaces. We prove that the proposed method converges strongly to a minimumnorm solution of the problem without using the conventional two cases approach. In addition, we present some numerical experiments to show the efficiency and applicability of the proposed method. The results obtained in this paper extend, generalize and improve several results in this direction.
Paper's Title:
Oscillatory Behavior of SecondOrder NonCanonical Retarded Difference Equations
Author(s):
G.E. Chatzarakis^{1}, N. Indrajith^{2}, E. Thandapani^{3} and K.S. Vidhyaa^{4}
^{1}Department
of Electrical and Electronic Engineering Educators,
School of Pedagogical and Technological Education,
Marousi 15122, Athens,
Greece.
Email: gea.xatz@aspete.gr,
geaxatz@otenet.gr
^{2}Department
of Mathematics,
Presidency College, Chennai  600 005,
India.
Email: indrajithna@gmail.com
^{3}Ramanujan
Institute for Advanced Study in Mathematics,
University of Madras,
Chennai  600 005,
India.
Email: ethandapani@yahoo.co.in
^{4}Department of
Mathematics,
SRM Easwari Engineering College,
Chennai600089,
India.
Email: vidyacertain@gmail.com
Abstract:
Using monotonic properties of nonoscillatory solutions, we obtain new oscillatory criteria for the secondorder noncanonical difference equation with retarded argument
Our oscillation results improve and extend the earlier ones. Examples illustrating the results are provided.
Paper's Title:
Simple Integral Representations for the Fibonacci and Lucas Numbers
Author(s):
Seán M. Stewart
Physical Science and Engineering Division,
King Abdullah
University of Science and Technology,
Thuwal 239556900,
Saudi
Arabia.
Email: sean.stewart@kaust.edu.sa
Abstract:
Integral representations of the Fibonacci numbers F_{kn + r} and the Lucas numbers L_{kn + r} are presented. Each is established using methods that rely on nothing beyond elementary integral calculus.
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