


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:
HyersUlamRassias Stability of a Generalized Jensen Functional Equation
Author(s):
A. Charifi, B. Bouikhalene, E. Elqorachi and A. Redouani
Department of
Mathematics, Faculty of Sciences,
Ibn Tofail University,
Kenitra, Morocco
charifi2000@yahoo.fr
bbouikhalene@yahoo.fr
Department of
Mathematics, Faculty of Sciences,
Ibn Zohr University,
Agadir, Morocco
elqorachi@hotmail.com
Redouaniahmed@yahoo.fr
Abstract:
In this paper we obtain the HyersUlamRassias stability for the generalized Jensen's functional equation in abelian group (G,+). Furthermore we discuss the case where G is amenable and we give a note on the HyersUlamstability of the Kspherical (n × n)matrix functional equation.
Paper's Title:
C*valued metric projection and MoorePenrose inverse on Hilbert C*modules
Author(s):
M. Eshaghi Gordji, H. Fathi and S.A.R. Hosseinioun
Department of Mathematics,
Semnan University, P.O. Box 35195363, Semnan,
Iran.
Center of Excellence in Nonlinear Analysis and Applications (CENAA),
Semnan University,
Iran.
Email: Madjid.Eshaghi@gmail.com
Department of Mathematics,
Shahid Beheshti University, Tehran,
Iran.
Email: Hedayat.fathi@yahoo.com
Department of Mathematical Sciences,
University of Arkansas, Fayetteville, Arkansas 72701,
USA.
Email: shossein@uark.net
Abstract:
Let t be a regular operator between Hilbert C^{*}modules and t^{†} be its MoorePenrose inverse. We give some characterizations for t^{†} based on C^{*}valued metric projection. MoorePenrose inverse of bounded operators and elements of a C^{*}algebra is studied as a special case.
Paper's Title:
Equivalence of the Nonsmooth Nonlinear Complementarity Problems to Unconstrained Minimization
Author(s):
M. A. Tawhid and J. L. Goffin
Department of Mathematics and Statistics,
School of Advanced Technologies and Mathematics,
Thompson Rivers University,
900 McGill Road, PO Box 3010, Kamloops, BC V2C 5N3
Canada
Alexandria University and Egypt Japan University of Science and Technology,
AlexandriaEgypt
mtawhid@tru.ca
Faculty of Management, McGill University,
1001 Sherbrooke Street West, Montreal, Quebec, H3A 1G5
Canada.
JeanLouis.Goffin@McGill.ca
Abstract:
This paper deals with nonsmooth nonlinear complementarity problem, where the underlying functions are nonsmooth which admit the Hdifferentiability but not necessarily locally Lipschitzian or directionally differentiable. We consider a reformulation of the nonlinear complementarity problem as an unconstrained minimization problem. We describe Hdifferentials of the associated penalized FischerBurmeister and Kanzow and Kleinmichel merit functions. We show how, under appropriate P_{0}, semimonotone (E_{0}), P, positive definite, and strictly semimonotone (E) conditions on an Hdifferential of f, finding local/global minimum of a merit function (or a `stationary point' of a merit function) leads to a solution of the given nonlinear complementarity problem. Our results not only give new results but also unify/extend various similar results proved for C^{1}.
Paper's Title:
Applications of Von Neumann Algebras to Rigidity Problems of (2Step) Riemannian (Nil)Manifolds
Author(s):
Atefeh HasanZadeh and HamidReza Fanai
DFouman Faculty of Engineering,
College of Engineering, University of Tehran,
Iran.
Email: hasanzadeh.a@ut.ac.ir
Department of Mathematical Sciences,
Sharif University of Technology,
Iran
Email: fanai@sharif.edu
Abstract:
In this paper, basic notions of von Neumann algebra and its direct analogues in the realm of groupoids and measure spaces have been considered. By recovering the action of a locally compact Lie group from a crossed product of a von Neumann algebra, other proof of one of a geometric propositions of O'Neil and an extension of it has been proposed. Also, using the advanced exploration of nilmanifolds in measure spaces and their corresponding automorphisms (Lie algebraic derivations) a different proof of an analytic theorem of Gordon and Mao has been attained. These two propositions are of the most important ones for rigidity problems of Riemannian manifolds especially 2step nilmanifolds.
Paper's Title:
Hankel Functional Connected to Lemniscate of Bernoulli
Author(s):
K. Ramanuja Rao, Rajnesh Lal and Kaushal Singh
Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
Email: ramanuja.kotti@fnu.ac.fj
rajnesh.lal@fnu.ac.fj
kaushal.singh@fnu.ac.fj
Abstract:
The aim of present paper is to derive a higher bound (HB) of 3^{rd} order Hankel determinant for a collection of holomorphic mappings connected with exactly to the right side of the lemniscate of Bernoulli, whose polar coordinates form is r^{2} = 2cos^{2}(2θ). The method carried in this paper is more refined than the method adopted by the authors (see [1]), who worked on this problem earlier.
Paper's Title:
On Closed Range C^{*}modular Operators
Author(s):
Javad FarokhiOstad and Ali Reza Janfada
Department of Mathematics,
Faculty of Mathematics and Statistics Sciences,
University of Birjand, Birjand,
Iran.
Email: j.farokhi@birjand.ac.ir
ajanfada@birjand.ac.ir
Abstract:
In this paper, for the class of the modular operators on Hilbert C^{*}modules, we give the conditions to closedness of their ranges. Also, the equivalence conditions for the closedness of the range of the modular projections on Hilbert C^{*}modules are discussed. Moreover, the mixed reverse order law for the MoorePenrose invertible modular operators are given.
Paper's Title:
FeketeSzegö Inequality for Sakaguchi Type of functions in Petal Shaped Domain
Author(s):
E. K. Nithiyanandham and B. Srutha Keerthi
Division of Mathematics, School of
Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai  600 048,
India.
Email: nithiyankrish@gmail.com
Division of Mathematics, School of
Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai  600 048,
India.
Email: keerthivitmaths@gmail.com
Abstract:
In this paper, we estimate coefficient bounds,a_2,a_3 and a_4, FeketeSzegö inequality and Toeplitz determinant T_{2}(2) and T_{3}(1) for functions belonging to the following class
the function being holomorphic, we expand using Taylor series and obtain several corollaries and consequences for the main result.
Paper's Title:
Toeplitz Determinant for Sakaguchi Type Functions Under Petal Shaped Domain
Author(s):
B. Nandhini and B. Srutha Keerthi
Division of Mathematics, School of
Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai  600 048,
India.
Email:
nandhinibaskar1996@gmail.com
Division of Mathematics, School of
Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai  600 048,
India.
Email: keerthivitmaths@gmail.com
Abstract:
We introduce a new general subclass GP^{t,ρ} of Sakaguchi kind function on a Petal shaped domain. We obtain coefficients bounds and upper bounds for the FeketeSzegö functional over the class. From these functions we obtain the bounds of first four coefficients, and then we have derived the Toeplitz determinant T_{2}(2) and T_{3}(1) whose diagonal entries are the coefficients of functions.
Paper's Title:
An Algorithm to Compute GaussianType Quadrature Formulae
that Integrate Polynomials and Some Spline Functions Exactly
Author(s):
Allal Guessab
Laboratoire de Mathématiques Appliquées,
Université de Pau, 64000, Pau,
France.
allal.guessab@univpau.fr
URL: http://www.univpau.fr/~aguessab/
Abstract:
It is wellknown that for sufficiently smooth integrands on an interval, numerical integration can be performed stably and efficiently via the classical (polynomial) Gauss quadrature formulae. However, for many other sets of integrands these quadrature formulae do not perform well. A very natural way of avoiding this problem is to include a wide class among arbitrary functions (not necessary polynomials) to be integrated exactly. The spline functions are natural candidates for such problems. In this paper, after studying Gaussian type quadrature formulae which are exact for spline functions and which contain boundary terms involving derivatives at both end points, we present a fast algorithm for computing their nodes and weights. It is also shown, taking advantage of the close connection with ordinary Gauss quadrature formula, that the latter are computed, via eigenvalues and eigenvectors of real symmetric tridiagonal matrices. Hence a new class of quadrature formulae can then be computed directly by standard software for ordinary Gauss quadrature formula. Comparative results with classical Gauss quadrature formulae are given to illustrate the numerical performance of the approach.
Paper's Title:
On an Autocorrection Phenomenon of the Eckhoff Interpolation
Author(s):
A. Poghosyan
Institute of Mathematics, National Academy
of Sciences,
24b Marshal Baghramian ave., Yerevan 0019,
Republic of Armenia
arnak@instmath.sci.am
Abstract:
The paper considers the KrylovLanczos and the Eckhoff interpolations of a function with a discontinuity at a known point. These interpolations are based on certain corrections associated with jumps in the first derivatives. In the Eckhoff interpolation, approximation of the exact jumps is accomplished by the solution of a system of linear equations. We show that in the regions where the 2periodic extension of the interpolated function is smooth, the Eckhoff interpolation converges faster compared with the KrylovLanczos interpolation. This accelerated convergence is known as the autocorrection phenomenon. The paper presents a theoretical explanation of this phenomenon. Numerical experiments confirm theoretical estimates.
Paper's Title:
Application of Equivalence Method to Classify MongeAmpère Equations of Elliptic Type
Author(s):
Moheddine Imsatfia
Email: imsatfia@math.jussieu.fr
Abstract:
In this paper, we apply Cartan's equivalence method to give a local classification of MongeAmpère equations of elliptic type. Then we find a necessary and sufficient conditions such that a MongeAmpère equation is either contactomorphic to the Laplace equation or to an EulerLagrange equation.
Paper's Title:
Optimization and Approximation for Polyhedra in Separable Hilbert Spaces
Author(s):
Paolo d'Alessandro
Department of Mathematics,
Third University of Rome,
Italy.
Email: pdalex45@gmail.com
Abstract:
This paper studies infinite dimensional polyhedra, covering the case in which range spaces of operators defining inequality systems are not closed. A rangespace method of linear programming is generalized to infinite dimensions and finite dimensional methods of approximation are introduced.
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:
A Comparison Between Two Different Stochastic Epidemic Models with Respect to the Entropy
Author(s):
Farzad Fatehi and Tayebe Waezizadeh
Department of Mathematics,
University of Sussex,
Brighton BN1 9QH,
UK.
Email: f.fatehi@sussex.ac.uk
URL:
http://www.sussex.ac.uk/profiles/361251
Department of Pure Mathematics, Faculty
of Mathematics and Computer,
Shahid Bahonar University of Kerman,
Kerman 7616914111,
Iran.
Email: waezizadeh@uk.ac.ir
URL:
http://academicstaff.uk.ac.ir/en/tavaezizadeh
Abstract:
In this paper at first a brief history of mathematical models is presented with the aim to clarify the reliability of stochastic models over deterministic models. Next, the necessary background about random variables and stochastic processes, especially Markov chains and the entropy are introduced. After that, entropy of SIR stochastic models is computed and it is proven that an epidemic will disappear after a long time. Entropy of a stochastic mathematical model determines the average uncertainty about the outcome of that random experiment. At the end, we introduce a chain binomial epidemic model and compute its entropy, which is then compared with the DTMC SIR epidemic model to show which one is nearer to reality.
Paper's Title:
The Influence of Fluid Pressure in Macromechanical Cochlear Model
Author(s):
F. E. Aboulkhouatem^{1}, F. Kouilily^{1}, N. Achtaich^{1}, N. Yousfi^{1} and M. El Khasmi^{2}
^{1}Department
of Mathematics and Computer Science, Faculty of Sciences
Ben M'sik, Hassan II University, Casablanca,
Morocco.
^{2}Department
of Biology, Faculty of Sciences
Ben M'sik, Hassan II University, Casablanca,
Morocco.
Email:
fatiaboulkhouatem@gemail.com
URL: http://www.fsb.univh2c.ma/
Abstract:
An increase of pressure in the structure of cochlea may cause a hearing loss. In this paper, we established the relationship between the fluid pressure and the amplitude of displacement of Basilar Membrane to clarify the mechanisms of hearing loss caused by increasing of this pressure. So, a mathematical cochlear model was formulated using finite difference method in order to explain and demonstrate this malfunction in passive model. Numerical simulations may be considered as helpful tools which may extend and complete the understanding of a cochlea dysfunction.
Paper's Title:
Global Analysis on Riemannian Manifolds
Author(s):
Louis Omenyi and Michael Uchenna
Department of Mathematics, Computer
Science, Statistics and Informatics,
Alex Ekwueme Federal University, NdufuAlike,
Nigeria.
Email: omenyi.louis@funai.edu.ng,
michael.uchenna@funai.edu.ng
URL: http://www.funai.edu.ng
Abstract:
In this paper, an exposition of the central concept of global analysis on a Riemannan manifold is given. We extend the theory of smooth vector fields from open subsets of Euclidean space to Riemannan manifolds. Specifically, we prove that a Riemannian manifold admits a unique solution for a system of ordinary differential equations generated by the flow of smooth tangent vectors. The idea of partial differential equations on Riemannian manifold is highlighted on the unit sphere.
Paper's Title:
Attempts to Define a BaumConnes Map Via Localization of Categories for Inverse Semigroups
Author(s):
Bernhard Burgstaller
Departamento de Matematica,
Universidade Federal de Santa Catarina,
CEP 88.040900 FlorianopolisSC,
Brasil.
Email:
bernhardburgstaller@yahoo.de
URL:
http://mathematik.work/bernhardburgstaller/index.html
Abstract:
An induction functor in inverse semigroup equivariant KKtheory is considered, and together with %a restriction functors certain results similar to those known from the Mackey machinery are shown. It is also verified that for any socalled Econtinuous inverse semigroup its equivariant KKtheory satisfies the universal property and is a triangulated category.
Paper's Title:
The Effect of Harvesting Activities on PreyPredator Fishery Model with Holling type II in Toxicant Aquatic Ecosystem
Author(s):
Moh Nurul Huda, Fidia Deny Tisna Amijaya, Ika Purnamasari
Department of Mathematics, Faculty of
Mathematics and Natural Science,
Mulawarman University,
Samarinda, East Kalimantan,75123
Indonesia.
Email: muh.nurulhuda@fmipa.unmul.ac.id
fidiadta@fmipa.unmul.ac.id
ika.purnamasari@fmipa.unmul.ac.id
Abstract:
This paper discussed preypredator fishery models, in particular by analysing the effects of toxic substances on aquatic ecosystems. It is assumed in this model, that the prey population is plankton and the predator population is fish.\ Interaction between the two populations uses the Holling type II function. The existence of local and global critical points of the system are shown and their stability properties are analysed. Furthermore, Bionomic equilibrium and optimal control of harvesting are discussed. Finally, numerical simulations have been carried out to show in the interpretation of results.
Paper's Title:
Optimization Techniques on Affine Differential Manifolds
Author(s):
Ali S Rasheed, Faik Mayah and Ahmed A H ALJumaili
Ministry of Higher Education and
Scientific Research,
Iraq.
Email: ahmedhashem@gmail.com
Department of Physics, College of
Sciences,
University of Wasit,
Iraq.
Email: faik.mayah@gmail.com
Abstract:
In addition to solid ground of Riemannian manifolds fundamentals, this article interviews some popular optimization methods on Riemannian manifolds. Several optimization problems can be better stated on manifolds rather than Euclidean space, such as interior point methods, which in turns based on selfconcordant functions (logarithmic barrier functions). Optimization schemes like the steepest descent scheme, the Newton scheme, and others can be extended to Riemannian manifolds. This paper introduces some Riemannian and nonRiemannian schemes on manifolds.
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:
On Trigonometric Approximation of Continuous Functions by Deferred Matrix Means
Author(s):
Xhevat Zahir Krasniqi
Faculty of Education,
University of Prishtina "Hasan Prishtina",
Avenue "Mother Theresa " no. 5, Prishtinë
10000,
Republic of Kosovo.
Email: xhevat.krasniqi@unipr.edu
URL:
https://staff.unipr.edu/profile/xhevatkrasniqi
Abstract:
In this paper, for the first time, we introduce the deferred matrix means which contain the wellknown generalized deferred Nörlund, deferred Nörlund, deferred Riesz, deferred Cesàro means introduced earlier by others, and a new class of sequences (predominantly a wider class than the class of Head Bounded Variation Sequences). In addition, using the deferred matrix means of Fourier series of a continuous function, we determine the degree of approximation of such function via its modulus of continuity and a positive mediate function.
Paper's Title:
Bicomplex Univalent Functions
Author(s):
Mohd Arif, Amjad Ali, Rajat Singh^{*} and Romesh Kumar
Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
Email: azizymaths@gmail.com
Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
Email: amjadladakhi687@gmail.com
Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
Email: ^{*}rajat.singh.rs634@gmail.com
Department of Mathematics,
University of Jammu,
Jammu And Kashmir,
India.
Email: romeshmath@gmail.com
Abstract:
In this paper we introduce bicomplex univalent functions and also discuss the properties of a specific class of univalent functions.
Paper's Title:
Coefficient Bounds for Sakaguchi Kind of Functions Associated with Sine Function
Author(s):
Serap Bulut, H. Priya and B. Srutha Keerth
Kocaeli University,
Faculty of Aviation and Space Sciences,
Arslanbey Campus, 41285 KartepeKocaeli,
Turkey.
Email: serap.bulut@kocaeli.edu.tr
Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus, Chennai  600 048,
India.
Email: priyaharikrishnan18@gmail.com,
priya.h2020@vitstudent.ac.in
Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus, Chennai  600 048,
India.
Email: keerthivitmaths@gmail.com,
sruthakeerthi.b@vit.ac.in
Abstract:
In this paper, we introduce a new general subclass of analytic functions with respect to symmetric points in the domain of sine function. We obtain sharp coefficient bounds and upper bounds for the FeketeSzegö functional. Also we get sharp bounds for the logarithmic coefficients of functions belonging to this new class.
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