Paper's Title:

On the Generalized Inverse over Integral Domains

Author(s):

Yaoming Yu and Guorong Wang

College of Education, Shanghai Normal University
Shanghai 200234
People's Republic of China.
yuyaoming@online.sh.cn
grwang@shnu.edu.cn

Abstract:

In this paper, we study further the generalized inverse of a matrix A over an integral domain. We give firstly some necessary and sufficient conditions for the existence of the generalized inverse , an explicit expression for the elements of the generalized inverse and an explicit expression for the generalized inverse , which reduces to the {1} inverse. Secondly, we verify that the group inverse, the Drazin inverse, the Moore-Penrose inverse and the weighted Moore-Penrose inverse are identical with the generalized inverse for an appropriate matrix G, respectively, and then we unify the conditions for the existence and the expression for the elements of the weighted Moore-Penrose inverse, the Moore-Penrose inverse, the Drazin inverse and the group inverse over an integral domain. Thirdly, as a simple application, we give the relation between some rank equation and the existence of the generalized inverse , and a method to compute the generalized inverse . Finally, we give an example of evaluating the elements of without calculating .

Paper's Title:

Some fixed point results in partial S-metric spaces

Author(s):

M. M. Rezaee, S. Sedghi, A. Mukheimer, K. Abodayeh, and Z. D. Mitrovic

Department of Mathematics, Qaemshahr Branch,
Islamic Azad University, Qaemshahr,
Iran.
E-mail: Rezaee.mohammad.m@gmail.com

Department of Mathematics, Qaemshahr Branch,
Islamic Azad University, Qaemshahr,
Iran.
E-mail: sedghi.gh@qaemiau.ac.ir

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: mukheimer@psu.edu.sa

Department of Mathematics and General Sciences,
Prince Sultan University, Riyadh,
KSA.
E-mail: kamal@psu.edu.sa

Nonlinear Analysis Research Group,
Faculty of Mathematics and Statistics,
Ton Duc Thang University, Ho Chi Minh City,
Vietnam.
E-mail: zoran.mitrovic@tdtu.edu.vn

Abstract:

We introduce in this article a new class of generalized metric spaces, called partial S-metric spaces. In addition, we also give some interesting results on fixed points in the partial S-metric spaces and some applications.

Paper's Title:

A New Relaxed Complex-valued b-metric Type and Fixed Point Results

Author(s):

P. Singh, V. Singh and T. C. M. 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:

In this paper, we study the existence and uniqueness of fixed point in complex valued b-metric spaces and introduce a new relaxed α, β Complex-valued b-metric type by relaxing the triangle inequality and determine whether the fixed point theorems are applicable in these spaces.

Paper's Title:

Refinement Inequalities Among Symmetric Divergence Measures

Author(s):

Inder Jeet Taneja

Departamento de Matemática,
Universidade Federal de Santa Catarina, 88.040-900
Florianópolis, Sc, Brazil
taneja@mtm.ufsc.br
URL: http://www.mtm.ufsc.br/~taneja

Abstract:

There are three classical divergence measures in the literature on information theory and statistics, namely, Jeffryes-Kullback-Leiber’s J-divergence, Sibson-Burbea-Rao’s Jensen- Shannon divegernce and Taneja’s arithemtic - geometric mean divergence. These bear an interesting relationship among each other and are based on logarithmic expressions. The divergence measures like Hellinger discrimination, symmetric χ²−divergence, and triangular discrimination are not based on logarithmic expressions. These six divergence measures are symmetric with respect to probability distributions. In this paper some interesting inequalities among these symmetric divergence measures are studied. Refinements of these inequalities are also given. Some inequalities due to Dragomir et al. [6] are also improved.

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.

Paper's Title:

Generalised Models for Torsional Spine Reconnection

Author(s):

Ali Khalaf Hussain Al-Hachami

Department of Mathematics,
College of Education For Pure Sciences,
Wasit University,
Iraq.
E-mail: alhachamia@uowasit.edu.iq

Abstract:

Three-dimensional (3D) null points are available in wealth in the solar corona, and the equivalent is probably going to be valid in other astrophysical situations. On-going outcomes from sun oriented perceptions and from reproductions propose that reconnection at such 3D nulls may assume a significant job in the coronal dynamics. The properties of the torsional spine method of magnetic reconnection at 3D nulls are researched. Kinematic model are created, which incorporate the term ηJ that is spatially localised around the null, stretching out along the spine of the null. The null point is to research the impact of shifting the level of asymmetry of the null point magnetic field on the subsequent reconnection process where past examinations constantly considered a non-nonexclusive radially symmetric null. Specifically we analyse the rate of reconnection of magnetic flux at the spine of null point. Logical arrangements are determined for the enduring kinematic equation, and contrasted and the after effects of torsional spine reconnection models when the current is restricted in which the Maxwell conditions are illuminated. The geometry of the current layers inside which torsional spine reconnection happen is autonomous on the symmetry of the magnetic field. Torsional spine reconnection happens in a thin cylinder around the spine, with circular cross-segment when the fan eigenvalues are extraordinary. The short axis of the circle being along the solid field bearing. Just as it was discovered that the fundamental structure of the method of attractive reconnection considered is unaffected by changing the magnetic field symmetry, that is, the plasma flow is discovered rotational around the spine of null point. The spatiotemporal pinnacle current, and the pinnacle reconnection rate achieved, are found not to rely upon the level of asymmetry.

Paper's Title:

Existence of Solution of Differential and Riemann-Liouville Equation Via Fixed Point Approach in Complex Valued b-Metric Spaces

Author(s):

K. Afassinou, A. A. Mebawondu, H. A. Abass and O. K. Narain

Department of Science Access,
University of Zululand, KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: dele@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: hammedabass548@gmail.com

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

Abstract:

In this paper, we establish some fixed point and common fixed point results for a new type of generalized contractive mapping using the notion of C-class function in the framework of complex valued b-metric spaces. As an application, we establish the existence and uniqueness of a solution for Riemann-Liouville integral and ordinary differential equation in the framework of a complete complex valued b-metric spaces. The obtained results generalize and improve some fixed point results in the literature.

Paper's Title:

Solving Strongly Nonlinear Fractional Fredholm Integral-Differential Equations in Caputo's Sense Using the SBA Method

Author(s):

Germain Kabore¹, Bakari Abbo², Ousseni So³ and Blaise Some¹

¹Laboratoire d'Analyse Numerique, Informatique et de Biomathmathiques (L.N.I.BIO),
Universite Joseph Ki-Zerbo,
Burkina Faso.
E-mail: germainkabore982@gmail.com, blaisesomeouaga1@gmail.com

²University of N'Damena, Tchad.
E-mail: bakariabbo@yahoo.fr

³Laboratoire d'Analyse Numerique, Informatique et de Biomathemathiques (L.N.I.BIO),
Ecole Normale Superieure,
Burkina Faso.
E-mail: sousseni@yahoo.fr

Abstract:

The work addressed in this article consists in constructing the exact solutions, where they exist, of fractional Fredholm-type integro-differential equations in the sense of Caputo. Our results are obtained using the SBA method. The simplification of the approach, the analysis of its convergence, and the generalization of this method to these types of highly nonlinear equations constitute our scientific contribution.

Paper's Title:

Contact With Adhesion between a Deformable Body and a Foundation

Author(s):

B. Teniou and M. Sofonea

Laboratoire de Mathematiques Appliquées et Modélisation,
Université Mentouri, Constantine 25000,
Algeria
tenioubou2@yahoo.fr

Laboratoire de Mathématiques et Physiques pour les Systémes,
Univesité de Perpignan,
France.
sofonea@univ-perp.fr
 

Abstract:

The aim of this work is study a dynamic contact problem between a deformable body and a foundation where the deformations are supposed to be small. The contact is with adhesion and normal compliance. The behavior of this body is modeled by a nonlinear elastic-visco-plastic law. The evolution of bonding field is described by a nonlinear differential equation. We derive a variational formulation of the contact problem and we prove the existence and uniqueness of its solution. The proof is based on the construction of three intermediate problems and then we construct a contraction mapping whose unique fixed point will be the weak solution of the mechanical problem.

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.

Paper's Title:

On Eigenvalues and Boundary Curvature of the C*-algebra Numerical Rang

Author(s):

M. T. Heydari

Department of Mathematics,
College of Sciences,
Yasouj University,
Yasouj, 75914-74831,
Iran.

E-mail: heydari@yu.ac.ir 

Abstract:

Let A be a C*-algebra with unit 1 and a∈A be a nilpotent. By Donoghue's Theorem, all corner points of its numerical range V(a) belong to the spectrum σ(a). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂ V(a) of V(a) to σ(a) should be in some sense bounded by the radius of curvature of ∂ V(a) at p.

Paper's Title:

Some New Inequalities of Hermite-Hadamard and Fejér Type for Certain Functions with Higher Convexity

Author(s):

Steven G. From

Department of Mathematics,
University of Nebraska at Omaha,
Omaha, Nebraska 68182-0243,
U.S.A.
E-mail: sfrom@unomaha.edu

Abstract:

In this paper, we present some new inequalities of Hermite-Hadamard or Fejér type for certain functions satisfying some higher convexity conditions on one or more derivatives.
An open problem is given also.
Some applications to the logarithmic mean are given.

Paper's Title:

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

Author(s):

Sever S. Dragomir^1,2

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.

Paper's Title:

Polyanalytic Functions on Subsets of Z[i]

Author(s):

Abtin Daghighi

Linköping University,
SE-581 83,
Sweden.

E-mail: abtindaghighi@gmail.com

Abstract:

For positive integers q we consider the kernel of the powers L^q where L is one of three kinds of discrete analogues of the Cauchy-Riemann operator. The first two kinds are well-studied, but the third kind less so. We give motivations for further study of the third kind especially since its symmetry makes it more appealing for the cases q≥ 2.

From an algebraic perspective it makes sense that the chosen multiplication on the kernels is compatible with the choice of pseudo-powers. We propose such multiplications together with associated pseudo-powers. We develop a proof-tool in terms of certain sets of uniqueness.

Paper's Title:

A New Adomian Approach to Solving Integral Equations of Fredholm and Volterra Second Kind

Author(s):

Ouedraogo Seny, Nebie Abdoul Wassiha, Youssouf Pare, Blaise Some

Departement de mathematiques,
Universite Joseph Ki-Zerbo,
Burkina Faso.
E-mail: oseny@yahoo.fr, nebwass@yahoo.fr
pareyoussouf@yahoo.fr, some@univ-ouaga.bf

Abstract:

In order to simplify the resolution of Fredholm and Volterra's second type integral equations, we propose a new approach based on the Adomian Decompositional Method (ADM). We test the new approach on several examples with success.

Paper's Title:

Reduced Generalized Combination Synchronization Between Two n-Dimensional Integer-Order Hyperchaotic Systems and One m-Dimensional Fractional-Order Chaotic System

Author(s):

Smail Kaouache, Mohammed Salah Abdelouahab and Rabah Bououden

Laboratory of Mathematics and their interactions,
Abdelhafid Boussouf University Center, Mila.
Algeria
E-mail: 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 n-dimensional integer-order hyperchaotic drive systems and one m-dimensional fractional-order chaotic response system. According to the stability theorem of fractional-order 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 fractional-order Rabinovich-Fabrikant chaotic system. Finally, numerical results are presented to fit our theoretical analysis.

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.
E-mail: 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 r² = 2cos²(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:

Using Direct and Fixed Point Technique of Cubic Functional Equation and its Hyers-Ulam Stability

Author(s):

Ramanuja Rao Kotti, Rajnesh Krishnan Mudaliar, Kaushal Neelam Devi, Shailendra Vikash Narayan

Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
E-mail: ramanuja.kotti@fnu.ac.fj
URL: https://www.fnu.ac.fj

Abstract:

In this present work, we introduce a new type of finite dimensional cubic functional equation of the form

where Φ≥4 is an integer, and derive its general solution. The main purpose of this work is to investigate the Hyers-Ulam stability results for the above mentioned functional equation in Fuzzy Banach spaces by means of direct and fixed point methods.

Paper's Title:

Portfolio Optimization of Sharia and Non-Sharia Stocks Using Single Index Model (Case study: Jakarta Sharia Index and Kompas 100 Index)

Author(s):

Kwardiniya Andawaningtyas, Muhammad Luthfi, Marjono, Endang Wahyu Handamari, Umu S'adah, Evi Ardiyani

Department of Mathematics,
Brawijaya University, Malang,
Indonesia.

Department of Mathematics,
IPB University, Bogor,
Indonesia.

E-mail: dina_math@ub.ac.id
muhammadluthfi@student.ub.ac.id
marjono@ub.ac.id
ewahyu-math@ub.ac.id
u.saadah@ub.ac.id
ardiyanievi@apps.ipb.ac.id

Abstract:

Stocks are instruments with high returns but also have increased risks. One way to overcome this risk is to form a stock portfolio. This study observed 30 sharia stocks listed on the Jakarta Islamic Index (JII) and 28 non-shariah stocks listed on the Kompas 100 Index from March 2020 to September 2022. The data used is the daily closing price of stocks, the number of stock dividends, and the daily closing price of the Jakarta Composite Index (JCI) from 3rd March 2020, to 31st August 2022. In addition, interest rate of Bank Indonesia Certificate (SBI) is used as risk-free rate. This study aims to optimize the sharia and non-sharia stocks portfolio using the Single Index Model (SIM), which will then be evaluated using the Sharpe, Treynor, and Jensen ratio. The result is that the optimal portfolio of sharia stocks have better performance than the optimal portfolio of non-sharia stocks based on the Treynor ratio. Meanwhile, the optimal portfolio of non-sharia stocks have better performance than the optimal portfolio of sharia stocks based on the Sharpe and Jensen ratio.

Paper's Title:

New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces

Author(s):

S. S. Dragomir

Abstract:

New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in the earlier paper [13]. Further, they are employed to establish new Grüss type inequalities. Finally, some natural integral inequalities are stated as well.

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

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:

Orthogonality and ε-Orthogonality in Banach Spaces

Author(s):

H. Mazaheri and S. M. Vaezpour

Faculty of Mathematics, Yazd University, Yazd, Iran
vaezpour@yazduni.ac.ir 
hmazaheri@yazduni.ac.ir 

Abstract:

A concept of orthogonality on normed linear space was introduced by Brickhoff, also the concept of ε-orthogonality was introduced by Vaezpour. In this note, we will consider the relation between these concepts and the dual of X. Also some results on best coapproximation will be obtained.