Paper's Title:

On Zeros of Diagonally Quasiconvex Multifunctions

Author(s):

Zoran D. Mitrović

Faculty of Electrical Engineering,
University of Banja Luka,
78000 Banja Luka, Patre 5
Bosnia and Herzegovina
zmitrovic@etfbl.net

Abstract:

In this paper, we extended the notion of diagonally quasiconvexity for multifunctions and established several existence results for zeros of diagonally quasiconvex multifunctions. As applications we obtain the results of fixed points, coincidence points and best approximations for multifunctions. Using our result we also prove the existence of solutions to the variational-like inequality problem and generalized vector equilibrium problem. The results of this paper generalize some known results in the literature.

Paper's Title:

On Vector Variational Inequality Problem in Terms of Bifunctions

Author(s):

C. S. Lalitha and Monika Mehta

Department of Mathematics, Rajdhani College,
University of Delhi, Raja Garden,
Delhi 110015, India
cslalitha@rediffmail.com

Department of Mathematics, Satyawati College,
University Of Delhi, Ashok Vihar,
Phase-III, Delhi 110052, India
mridul_in@yahoo.com

Abstract:

In this paper, we consider a generalized vector variational inequality problem expressed in terms of a bifunction and establish existence theorems for this problem by using the concepts of cone convexity and cone strong quasiconvexity and employing the celebrated Fan's Lemma. We also give two types of gap functions for this problem.

Paper's Title:

Additive Mappings on Semiprime Rings Functioning as Centralizers

Author(s):

Abu Zaid Ansari and Faiza Shujat

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah, Madinah
K.S.A.
E-mail: ansari.abuzaid@gmail.com, ansari.abuzaid@iu.edu.sa

Department of Mathematics,
Faculty of Science,
Taibah University, Madinah,
K.S.A.
E-mail: faiza.shujat@gmail.com, fullahkhan@taibahu.edu.sa

Abstract:

The objective of this research is to prove that an additive mapping T:R → R is a centralizer on R if it satisfies any one of the following identities:

for all x ∈ R, where n ≥ 1 is a fixed integer and R is any suitably torsion free semiprime ring. Some results on involution "*" are also presented as consequences of the main theorems. In addition, we will take criticism in account with examples.

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:

On Automorphisms and Bi-derivations of Semiprime Rings

Author(s):

Abu Zaid Ansari, Faiza Shujat, Ahlam Fallatah

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah, Madinah
K.S.A.
E-mail: ansari.abuzaid@gmail.com, ansari.abuzaid@iu.edu.sa

Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: faiza.shujat@gmail.com, fullahkhan@taibahu.edu.sa

Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: Afallatah@taibahu.edu.sa
 

Abstract:

In this article, our goal is to figure out a functional equation involving automorphisms and bi-derivations on certain semiprime ring. Also, we characterize the structure of automorphism, in case of prime rings.

Paper's Title:

Solving Fixed Point Problems and Variational Inclusions Using Viscosity Approximations

Author(s):

P. Patel, R. Shukla

Department of Mathematics, School of Advanced Sciences, VIT-AP University\\
Amaravati, 522237, Andhra Pradesh,
India.
E-mail: prashant.patel9999@gmail.com, prashant.p@vitap.ac.in

Department of Mathematical Sciences & Computing, Walter Sisulu University,
Mthatha 5117,
South Africa.
E-mail: rshukla@wsu.ac.za

Abstract:

This paper proposes a new algorithm to find a common element of the fixed point set of a finite family of demimetric mappings and the set of solutions of a general split variational inclusion problem in Hilbert spaces. The algorithm is based on the viscosity approximation method, which is a powerful tool for solving fixed point problems and variational inclusion problems. Under some conditions, we prove that the sequence generated by the algorithm converges strongly to this common solution.

Paper's Title:

A Reverse of the Triangle Inequality in Inner Product Spaces and Applications for Polynomials

Author(s):

I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić

Department of Applied Mathematics, Faculty of Electrical Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr

School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir

Faculty of Applied Technical Sciences, University of Prishtina,
Mother Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com

Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr

Abstract:

A reverse of the triangle inequality in inner product spaces related to the celebrated Diaz-Metcalf inequality with applications for complex polynomials is given.

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.

Paper's Title:

A New Method with Regularization for Solving Split Variational Inequality Problems in Real Hilbert Spaces

Author(s):

Francis Akutsah¹ and Ojen Kumar Narain²

¹School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216040405@stu.ukzn.ac.za, akutsah@gmail.com

 ²School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 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 minimum-norm 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:

Timelike Surfaces with a Common Line of Curvature in Minkowski 3-Space

Author(s):

M.K. Saad, A.Z. Ansari, M. Akram and F. Alharbi

Department of Mathematics ,
Faculty of Science,
Islamic University of Madinah,
KSA

Abstract:

In this paper, we analyze the problem of constructing a timelike surface family from a given non-null curve line of curvature. Using the Frenet frame of the non-null curve in Minkowski space E₁³  we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for the coefficients to satisfy both the line of curvature and the isoparametric requirements. In addition, a necessary and sufficient condition for the given non-null curve to satisfy the line of curvature and the geodesic requirements is investigated. The extension to timelike surfaces of revolution is also outlined. Meanwhile, some representative non-null curves are chosen to construct the corresponding timelike surfaces which possessing these curves as lines of curvature. Results presented in this paper have applications in geometric modeling and the manufacturing of products. In addition, some computational examples are given and plotted.

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.

Paper's Title:

Para-chaotic Tuples of Operators

Author(s):

Bahmann Yousefi and Javad Izadi

Department of Mathematics,
Payame Noor University,
P.O. Box 19395-3697, Tehran,
Iran
b_yousefi@pnu.ac.ir
javadie2003@yahoo.com

Abstract:

In this paper, we introduce para-chaotic tuples of operators and we give some relations between para-chaoticity and Hypercyclicity Criterion for a tuple of operators.

Paper's Title:

A new approach to the study of fixed point for simulation functions with application in G-metric spaces

Author(s):

Komi Afassinou and Ojen Kumar Narain

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

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

Abstract:

The purpose of this work is to generalize the fixed point results of Kumar et al. [11] by introducing the concept of (α,β)-Z-contraction mapping, Suzuki generalized (α,β)-Z-contraction mapping, (α,β)-admissible mapping and triangular (α,β)-admissible mapping in the frame work of G-metric spaces. Fixed point theorems for these class of mappings are established in the frame work of a complete G-metric spaces and we establish a generalization of the fixed point result of Kumar et al. [11] and a host of others in the literature. Finally, we apply our fixed point result to solve an integral equation.

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:

Composite Variational-Like Inequalities Given By Weakly Relaxed ζ-Semi-Pseudomonotone Multi-Valued Mapping

Author(s):

Syed Shakaib Irfan, Iqbal Ahmad, Zubair Khan and Preeti Shukla

College of Engineering, Qassim University
Buraidah, Al-Qassim,
Saudi Arabia.
E-mail: shakaib@qec.edu.sa

College of Engineering, Qassim University
Buraidah, Al-Qassim,
Saudi Arabia.
E-mail: iqbal@qec.edu.sa

Department of Mathematics,
Integral University Lucknow,
India.
E-mail: zkhan@iul.ac.in

Department of Mathematics,
Integral University Lucknow,
India.
E-mail: shuklapreeti1991@gmail.com

Abstract:

In this article, we introduce a composite variational-like inequalities with weakly relaxed ζ-pseudomonotone multi-valued maping in reflexive Banach spaces. We obtain existence of solutions to the composite variational-like inequalities with weakly relaxed ζ-pseudomon -otone multi-valued maps in reflexive Banach spaces by using KKM theorem. We have also checked the solvability of the composite variational-like inequalities with weakly relaxed ζ-semi-pseudomonotone multi-valued maps in arbitrary Banach spaces using Kakutani-Fan-Glicksberg fixed point theorem.

Paper's Title:

A Self Adaptive Method for Solving Split Bilevel Variational Inequalities Problem in Hilbert Spaces

Author(s):

Francis Akutsah¹, Ojen Kumar Narain², Funmilayo Abibat Kasali³ Olawale Kazeem Oyewole⁴ and Akindele Adebayo Mebawondu⁵

¹School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216040405@stu.ukzn.ac.za, akutsah@gmail.com

²School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa. 
E-mail: naraino@ukzn.ac.za

³Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: fkasali@mtu.edu.ng

⁴Technion-Israel Institute of Technology.
E-mail: 217079141@stu.ukzn.ac.za, oyewoleolawalekazeem@gmail.co

⁵School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa. 
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: 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 α-strongly 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.

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