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28: Paper Source PDF document

Paper's Title:

Maximal Inequalities for Multidimensionally Indexed Demimartingales and the Hájek-Rényi Inequality for Associated Random Variables

Author(s):

Tasos C. Christofides and Milto Hadjikyriakou

Department of Mathematics and Statistics
University of Cyprus
P.O.Box 20537, Nicosia 1678, Cyprus

tasos@ucy.ac.cy
miltwh@gmail.com

Abstract:

Demimartingales and demisubmartingales introduced by Newman and
Wright (1982) generalize the notion of martingales and
submartingales respectively. In this paper we define
multidimensionally indexed demimartingales and demisubmartingales
and prove a maximal inequality for this general class of random
variables. As a corollary we obtain a Hájek-Rényi inequality
for multidimensionally indexed associated random variables, the bound of which, when reduced to the case of single index, is sharper than the bounds already known in the literature.



22: Paper Source PDF document

Paper's Title:

Weak solutions of non coercive stochastic Navier-Stokes equations in R2

Author(s):

Wilhelm Stannat and Satoshi Yokoyama

Technische Universität Berlin,
Strasse des 17. Juni 136, 10623 Berlin,
Germany.

Graduate School of Mathematical Sciences,
The University of Tokyo,
Komaba, Tokyo 153-8914,
Japan.

E-mail: stannat@math.tu-berlin.de

E-mail: satoshi2@ms.u-tokyo.ac.jp

Abstract:

We prove existence of weak solutions of stochastic Navier-Stokes equations in R2 which do not satisfy the coercivity condition. The equations are formally derived from the critical point of some variational problem defined on the space of volume preserving diffeomorphisms in R2. Since the domain of our equation is unbounded, it is more difficult to get tightness of approximating sequences of solutions in comparison with the case of a bounded domain. Our approach is based on uniform a priori estimates on the enstrophy of weak solutions of the stochastic 2D-Navier-Stokes equations with periodic boundary conditions, where the periodicity is growing to infinity combined with a suitable spatial cutoff-technique.



9: Paper Source PDF document

Paper's Title:

A note on Inequalities due to Martins, Bennett and Alzer

Author(s):

József Sándor

Babeş-Bolyai University of Cluj, Department of Mathematics and Computer Sciences
Kogălniceanu Nr.1, Cluj-Napoca,
Romania.
jjsandor@hotmail.com
jsandor@member.ams.org


Abstract:

A short history of certain inequalities by Martins, Bennett as well as Alzer, is provided. It is shown that, the inequality of Alzer for negative powers [6], or Martin's reverse inequality [7] are due in fact to Alzer [2]. Some related results, as well as a conjecture, are stated.



7: Paper Source PDF document

Paper's Title:

Reverse of Martin's Inequality

Author(s):

Chao-Ping Chen, Feng Qi, and Sever S. Dragomir

Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010, China
chenchaoping@sohu.com; chenchaoping@hpu.edu.cn 

Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University,
Jiaozuo City, Henan 454010, China
qifeng@hpu.edu.cn 
Url: http://rgmia.vu.edu.au/qi.html

School of Computer Science and Mathematics,
Victoria University of Technology,
P. O. Box 14428, Melbourne City Mc,
Victoria 8001, Australia
Sever.Dragomir@vu.edu.au 
Url: http://rgmia.vu.edu.au/SSDragomirWeb.html
 

Abstract:

In this paper, it is proved that

for all natural numbers n, and all real r < 0.



5: Paper Source PDF document

Paper's Title:

Iterative Approximation of Zeros of Accretive Type Maps, with Applications

Author(s):

Charles Ejike Chidume, Chinedu Godwin Ezea, and Emmanuel Ezzaka Otubo

African University of Science and Technology, Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng
E-mail: chinedu.ezea@gmail.com
E-mail: mrzzaka@yahoo.com

Department of Mathematics,
Nnamdi Azikiwe University,
Awka,
Nigeria
E-mail: chinedu.ezea@gmail.com

Ebonyi State University,
Abakaliki,
Nigeria
E-mail: mrzzaka@yahoo.com

Abstract:

Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm. Let J:E E* be the normalized duality map on E and let A:E* E be a map such that AJ is an accretive and uniformly continuous map. Suppose that (AJ)-1(0) in nonempty. Then, an iterative sequence is constructed and proved to converge strongly to some u* in (AJ)-1(0). Application of our theorem in the case that E is a real Hilbert space yields a sequence which converges strongly to a zero of A. Finally, non-trivial examples of maps A for which AJ is accretive are presented..



4: Paper Source PDF document

Paper's Title:

On Subspace-Supercyclic Operators

Author(s):

Mansooreh Moosapoor

Assistant Professor,
Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: mosapor110@gmail.com m.mosapour@cfu.ac.ir

Abstract:

In this paper, we prove that supercyclic operators are subspace-supercyclic and by this we give a positive answer to a question posed in ( L. Zhang, Z. H. Zhou, Notes about subspace-supercyclic operators, Ann. Funct. Anal., 6 (2015), pp. 60--68). We give examples of subspace-supercyclic operators that are not subspace-hypercyclic. We state that if T is an invertible supercyclic operator then Tn and T-n is subspace-supercyclic for any positive integer n. We give two subspace-supercyclicity criteria. Surprisingly, we show that subspace-supercyclic operators exist on finite-dimensional spaces.



4: Paper Source PDF document

Paper's Title:

Some criteria for Subspace-hypercyclicity of C0-semigroups

Author(s):

Mansooreh Moosapoor

Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: m.mosapour@cfu.ac.ir
mosapor110@gmail.com
 

Abstract:

We research subspace-hypercyclic C0-semigroups in this paper. We present various types of subspace-hypercyclicity criteria for C0-semigroups. Some of them are stronger than the criteria introduced before. Also, we state that if a C0-semigroup (Tt}t 0 satisfies in any of them, then (Tt⊕Tt}t 0 is subspace-hypercyclic.



3: Paper Source PDF document

Paper's Title:

Oscillation and Boundedness of Solutions to First and Second Order Forced Dynamic Equations with Mixed Nonlinearities

Author(s):

Ravi P. Agarwal and Martin Bohner

Department of Mathematical Sciences, Florida Institute of Technology
Melbourne, FL 32901,
U.S.A.
bohner@mst.edu
URL:http://web.mst.edu/~bohner

Department of Economics and Finance, Missouri University of Science and Technology
Rolla, MO 65401,
U.S.A.
agarwal@fit.edu


Abstract:

Some oscillation and boundedness criteria for solutions to certain first and second order forced dynamic equations with mixed nonlinearities are established. The main tool in the proofs is an inequality due to Hardy, Littlewood and Pólya. The obtained results can be applied to differential equations, difference equations and q-difference equations. The results are illustrated with numerous examples.



3: Paper Source PDF document

Paper's Title:

Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF 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 real-valued 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.



3: Paper Source PDF document

Paper's Title:

Inequalities for Discrete F-Divergence Measures: A Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF 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:

In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated f-divergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of Kullback-Leibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the f-divergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.



3: Paper Source PDF document

Paper's Title:

The Conservativeness of Girsanov Transformed for Symmetric Jump-diffusion Process

Author(s):

Mila Kurniawaty and Marjono

Department of Mathematics,
Universitas Brawijaya,
Malang,
Indonesia.
E-mail: mila_n12@ub.ac.id, marjono@ub.ac.id

Abstract:

We study about the Girsanov transformed for symmetric Markov processes with jumps associated with regular Dirichlet form. We prove the conservativeness of it by dividing the regular Dirichlet form  into the "small jump" part and the "big jump" part.



2: Paper Source PDF document

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 88003-8001
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.



2: Paper Source PDF document

Paper's Title:

Asymptotic Distribution of Products of Weighted Sums of Dependent Random Variables

Author(s):

Y. Miao and J. F. Li

College of Mathematics and Information Science,
Henan Normal University
Henan, China
yumiao728@yahoo.com.cn

College of Mathematics and Information Science,
Henan Normal University, 453007
Henan, China.
junfen_li@yahoo.com.cn

Abstract:

In this paper we establish the asymptotic distribution of products of weighted sums of dependent positive random variable, which extends the results of Rempała and Wesołowski (2002).



2: Paper Source PDF document

Paper's Title:

Examples of Fractals Satisfying the Quasihyperbolic Boundary Condition

Author(s):

Petteri Harjulehto and Riku Klén

Department of Mathematics and Statistics,
FI-20014 University of Turku,
Finland

E-mail: petteri.harjulehto@utu.fi

E-mail: riku.klen@utu.fi

Abstract:

In this paper we give explicit examples of bounded domains that satisfy the quasihyperbolic boundary condition and calculate the values for the constants. These domains are also John domains and we calculate John constants as well. The authors do not know any other paper where exact values of parameters has been estimated.



2: Paper Source PDF document

Paper's Title:

Strong Convergence Theorem for a Common Fixed Point of an Infinite Family of J-nonexpansive Maps with Applications

Author(s):

Charlse Ejike Chidume, Otubo Emmanuel Ezzaka and Chinedu Godwin Ezea

African University of Science and Technology,
Abuja,
Nigeria.
E-mail: cchidume@aust.edu.ng

Ebonyi State University,
Abakaliki,
Nigeria.
E-mail: mrzzaka@yahoo.com

 Nnamdi Azikiwe University,
Awka,
Nigeria.
E-mail: chinedu.ezea@gmail.com

Abstract:

Let E be a uniformly convex and uniformly smooth real Banach space with dual space E*. Let {Ti}i=1 be a family of J-nonexpansive maps, where, for each i,~Ti maps E to 2E*. A new class of maps, J-nonexpansive maps from E to E*, an analogue of nonexpansive self maps of E, is introduced. Assuming that the set of common J-fixed points of {Ti}i=1 is nonempty, an iterative scheme is constructed and proved to converge strongly to a point x* in n=1FJTi. 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.



2: Paper Source PDF document

Paper's Title:

A Multivalued Version of the Radon-Nikodym Theorem, via the Single-valued Gould Integral

Author(s):

Domenico Candeloro1, Anca Croitoru2, Alina Gavriluţ2, Anna Rita Sambucini1

1Dept. of Mathematics and Computer Sciences,
University of Perugia,
1, Via Vanvitelli -- 06123, Perugia,
Italy.
E-mail:  domenico.candeloro@unipg.it, anna.sambucini@unipg.it

2Faculty of Mathematics,
Al. I. Cuza University,
700506 Iaşi,
Romania.
E-mail: croitoru@uaic.ro, gavrilut@uaic.ro

Abstract:

In this paper we consider a Gould type integral of real functions with respect to a compact and convex valued not necessarily additive measure. In particular we will introduce the concept of integrable multimeasure and, thanks to this notion, we will establish an exact Radon-Nikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.



2: Paper Source PDF document

Paper's Title:

ψ(m,q)-Isometric Mappings on Metric Spaces

Author(s):

Sid Ahmed Ould Beinane, Sidi Hamidou Jah and Sid Ahmed Ould Ahmed Mahmoud

Mathematical Analysis and Applications, Mathematics Department, College of Science,
Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
E-mail: beinane06@gmail.com

Department of Mathematics, College of Science Qassim University,
P.O. Box 6640, Buraydah 51452,
Saudi Arabia.
E-mail: jahsiidi@yahoo.fr

Mathematical Analysis and Applications,
Mathematics Department, College of Science, Jouf University,
Sakaka P.O.Box 2014,
Saudi Arabia.
E-mail: sidahmed@ju.edu.sa, sidahmed.sidha@gmail.com

Abstract:

The concept of (m,p)-isometric operators on Banach space was extended to (m,q)-isometric mappings on general metric spaces in [6]. This paper is devoted to define the concept of ψ(m, q)-isometric, which is the extension of A(m, p)-isometric operators on Banach spaces introduced in [10]. Let T,ψ: (E,d) -> (E, d) be two mappings.
For some positive integer m and q (0,). T is said to be an ψ(m,q)-isometry, if for all  y,z E,



1: Paper Source PDF document

Paper's Title:

On Positive Entire Solutions of Second Order Quasilinear Elliptic Equations

Author(s):

Zuodong Yang and Honghui Yin

Institute of Mathematics, School of Mathematics and Computer Science,
Nanjing Normal University, Jiangsu Nanjing 210097,
China;
zdyang_jin@263.net

Department of Mathematics, Huaiyin Teachers College,
Jiangsu Huaian 223001,
China;
School of Mathematics and Computer Sciences,
Nanjing Normal University, Jiangsu Nanjing 210097,
China.
yin_hh@sina.com


Abstract:

In this paper, our main purpose is to establish the existence theorem of positive entire solutions of second order quasilinear elliptic equations under new conditions. The main results of the present paper are new and extend the previously known results.



1: Paper Source PDF document

Paper's Title:

Approximation of Derivatives in a Singularly Perturbed Second Order Ordinary Differential Equation with Discontinuous Terms Arising in Chemical Reactor Theory

Author(s):

R. Mythili Priyadharshini and N. Ramanujam

Department of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, India.
matram2k3@yahoo.com
URL: http://www.bdu.ac.in/depa/science/ramanujam.htm

Abstract:

In this paper, a singularly perturbed second order ordinary differential equation with a discontinuous convection coefficient arising in chemical reactor theory is considered. A robust-layer-resolving numerical method is suggested. An ε-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are provided to illustrate the theoretical results.



1: Paper Source PDF document

Paper's Title:

Solving Fractional Transport Equation via Walsh Function

Author(s):

A. Kadem

L. M. F. N., Mathematics Department,
 University of Setif,
Algeria
abdelouahak@yahoo.fr
 

Abstract:

In this paper we give a complete proof of A method for the solution of fractional transport equation in three-dimensional case by using Walsh function is presented. The main characteristic of this technique is that it reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem.



1: Paper Source PDF document

Paper's Title:

On the Boundedness of Hardy's Averaging Operators

Author(s):

Dah-Chin Luor

Department of Applied Mathematics,
I-Shou University, Dashu District,
Kaohsiung City 84001,
Taiwan, R.O.C.
dclour@isu.edu.tw

Abstract:

In this paper we establish scales of sufficient conditions for the boundedness of Hardy's averaging operators on weighted Lebesgue spaces. The estimations of the operator norms are also obtained. Included in particular are the Erdélyi-Kober operators.



1: Paper Source PDF document

Paper's Title:

A Dynamic Contact Problem for an Electro Viscoelastic Body

Author(s):

Denche M. and Ait Kaki L.

Laboratoire Equations Differentielles,
Departement de Mathematiques,
Universite Constantine 1,
Algeria.

Ecole Normale Superieure,
Departement des Sciences Exactes et Informatique,
Plateau Mansourah, Constantine.
Algeria.

E-mail: m.denche@umc.edu.dz
leilaitkaki@yahoo.fr

Abstract:

We consider a dynamic problem which describes a contact between a piezoelectric body and a conductive foundation. The frictionless contact is modelled with the normal compliance, the electric conditions are supposed almost perfect. We prove the existence of a unique weak solution for almost perfect electric contact.



1: Paper Source PDF document

Paper's Title:

Scope of the Logarithmic Mean

Author(s):

Murali Rao and Agnish Dey

Department of Mathematics,
University of Florida,
1400 Stadium Road, Gainesville,
Florida 32611,
U. S. A.

E-mail: mrao@ufl.edu

URL: http://people.clas.ufl.edu/mrao

E-mail: agnish@ufl.edu

URL: http://people.clas.ufl.edu/agnish 

Abstract:

A number a is between two numbers x and y if and only if a is a convex combination of x and y, in other words, it is a "weighted mean" of x and y. Geometric mean, arithmetic mean are well known examples of these "means". Of more recent vintage is the logarithmic mean which has been considered in many articles in the literature. In this note, we first discuss some of its properties. Then we shall introduce the L function and explore the inverse of this function and its connection with the Lambert's Omega function.



1: Paper Source PDF document

Paper's Title:

MSplit Equality for Monotone Inclusion Problem and Fixed Point Problem in Real Banach Spaces

Author(s):

1,2Christian Chibueze Okeke, 3Abdumalik Usman Bello, 1Chinedu Izuchukwu, and 1Oluwatosin Temitope Mewomo

1School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: okekec@ukzn.ac.za
E-mail: izuchukwuc@ukzn.ac.za
E-mail: mewomoo@ukzn.ac.za

2DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-Mass)
Johannesburg,
South Africa.

3Federal University,
Dutsin-Ma, Katsina State,
Nigeria.
E-mail: uabdulmalik@fudutsinma.edu.ng

Abstract:

In this paper a new iterative algorithm for approximating a common solution of split equality monotone inclusion problem and split equality fixed point problem is introduced. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a split equality monotone inclusion problem and the set of solutions of a split equality fixed point problem for right Bregman strongly nonexpansive mappings in the setting of p-uniformly convex Banach spaces which are also uniformly smooth. We also give some applications.



1: Paper Source PDF document

Paper's Title:

Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions

Author(s):

Xiang Gao, Meera Sitharam, Adrian E. Roitberg

Department of Chemistry, and Department of Computer & Information Science & Engineering,
University of Florida,
Gainesville, FL 32611,
USA.
E-mail: qasdfgtyuiop@gmail.com
URL: https://scholar.google.com/citations?user=t2nOdxQAAAAJ

Abstract:

This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The bounds depend only on growth properties of the function and specific moments of the random variable. The bounds are particularly useful for distributions that are concentrated around the mean, a commonly occurring scenario such as the average of i.i.d. samples and in statistical mechanics.



1: Paper Source PDF document

Paper's Title:

The Jacobson Density Theorem for Non-Commutative Ordered Banach Algebras

Author(s):

Kelvin Muzundu

University of Zambia,
Deparment of Mathematics and Statistics,
P.O. Box 32379, Lusaka,
Zambia.
E-mail: kmzundu@gmail.com

Abstract:

The Jacobson density theorem for general non-commutative Banach algebras states as follows: Let π be a continuous, irreducible representation of a non-commutative Banach algebra A on a Banach space X. If x1,x2,...,xn are linearly independent in X and if y1,y2,...,yn are in X, then there exists an a A such that π(a)xi=yi for i=1,2,...,n. By considering ordered Banach algebras A and ordered Banach spaces X, we shall establish an order-theoretic version of the Jacobson density theorem.



1: Paper Source PDF document

Paper's Title:

A New Relaxed b-metric Type and Fixed Point Results

Author(s):

P. Singh, V. Singh and Thokozani Cyprian Martin Jele

Department of Mathematics,
University of KwaZulu-Natal,
Private Bag X54001, Durban,
South Africa.
E-mail: singhp@ukzn.ac.za, singhv@ukzn.ac.za, thokozani.jele@nwu.ac.za

Abstract:

The purpose of this paper is to introduce a new relaxed α, β b-metric type by relaxing the triangle inequality. We investigate the effect that this generalization has on fixed point theorems.



1: Paper Source PDF document

Paper's Title:

Generalized Von Neumann-Jordan Constant for Morrey Spaces and Small Morrey Spaces

Author(s):

H. Rahman and H. Gunawan

Department of Mathematics,
Islamic State University Maulana Malik Ibrahim Malang,
Jalan Gajayana No.50,
Indonesia.
E-mail: hairur@mat.uin-malang.ac.id

Analysis and Geometry Group,
Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
E-mail: hgunawan@math.itb.ac.id
URL:  http://personal.fmipa.itb.ac.id/hgunawan/

Abstract:

In this paper we calculate some geometric constants for Morrey spaces and small Morrey spaces, namely generalized Von Neumann-Jordan constant, modified Von Neumann-Jordan constants, and Zbaganu constant. All these constants measure the uniformly nonsquareness of the spaces. We obtain that their values are the same as the value of Von Neumann-Jordan constant for Morrey spaces and small Morrey spaces.



1: Paper Source PDF document

Paper's Title:

Lie Group Theoretic Approach of One-Dimensional Black-Scholes Equation

Author(s):

P. L. Zondi and M. B. Matadi

Department of Mathematical sciences,
Faculty of Sciences & Agriculture, University of Zululand,
P Bag X1001, Kwa-Dlangezwa 3886,
South Africa.
E-mail: matadim@unizulu.ac.za
zondip@unizulu.ac.za

Abstract:

This study discusses the Lie Symmetry Analysis of Black-Scholes equation via a modified local one-parameter transformations. It can be argued that the transformation of the Black-Scholes equation is firstly obtained by means of riskless rate. Thereafter, the corresponding determining equations to the reduced equation are found. Furthermore, new symmetries of the Black-Scholes equation are constructed and lead to invariant solutions.


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