# Ojen NarainUniversity of KwaZulu-Natal | ukzn · School of Mathematics, Statistics and Computer Science

Ojen Narain

Doctor of Philosophy

Postgraduate supervisor

## About

52

Publications

4,735

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72

Citations

Citations since 2017

Introduction

Senior Lecturer at the School Mathematics, Statistics and Computer Science - University of KwaZulu-Natal, Westville Campus

## Publications

Publications (52)

In this paper, we study a modified relaxed inertial Mann-type iterative algorithm for solving split monotone variational inclusion problem without prior knowledge of the bounded linear operator norm in real Hilbert spaces. Under some appropriate assumptions on the parameters, we established a strong convergence result of the proposed algorithm. As...

This paper considers an alternated inertial-type extrapolation algorithm for solving bilevel pseu-domonotone variational inequality problem in the framework of real Hilbert spaces with split variational inequality , and fixed points constraints of demimetric mapping. The algorithm which involves alternated inertial uses self-adjustment stepsize con...

This paper was published in Numerical Algebra, Control and Optimization. In this work, we propose a new inertial method for solving strongly monotone variational inequality problems over the solution set of a split variational inequality and composed fixed point problem in real Hilbert spaces. Our method uses stepsizes that are generated at each it...

Published in Australian Journal of Mathematical Analysis and Applications. 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 continuou...

To be published in Sahand Communications in Mathematical Analysis. In this paper, we introduce a new type of modified generalized α-nonexpansive mapping, establish some fixed points properties and demiclosedness principle for this class of mappings in the framework of uniformly convex Banach spaces. We further propose a new iterative method for app...

Published in Nonlinear Functional Analysis and Applications. In this paper, we introduce and study an iterative technique for solving quasi-monotone split variational inequality problems and fixed point problem in the framework of real Hilbert spaces. Our proposed iterative technique is self adaptive, and easy to implement. We establish that the pr...

To be published in Nonlinear Functional Analysis and Applications. In this paper, we study an iterative algorithm that is based on inertial prox-imal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spac...

In this paper, we study an iterative algorithm based on the modified inertial Tseng's method with viscosity approximation method for solving pseudomonotone variational inequality and split common fixed point of demimetric mappings problems without prior knowledge of the bounded linear operator norm in real Hilbert spaces. We established a strong co...

In this paper, we first introduce the Halpern iteration process for approximating the solution of the fixed point problem of a finite family of $k$-strictly pseudo-contractive mappings in Hadamard spaces. We also propose an extragradient Halpern iterative algorithm for approximating a common solution of a finite family of $k_j$-strictly pseudocontr...

In this article, we introduce the multiple-sets split equality variational inequality problem which includes the split feasibility problem, split variational inequality problem, split equality problem and multiple-sets split variational inequality problem to mention a few. Also, we prove a strong convergence theorem for approximation the solution o...

Published in Linear and Nonlinear Analyis. In this paper, using the concept of gate condition for multi-valued mappings, we introduce a modified proximal point algorithm combined with a Halpern iteration process for approximating a common element of the set of minimizers of a finite family of convex functions and common fixed points of a family of...

In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solution of split generalized equilibrium problem which is also fixed point of Bregman relatively nonexpansive mapping in $p$-uniformly convex Banach spaces which are also uniformly smooth. Our iterative method uses step-size which does...

In this paper, we further develop the notion of cyclic (α, β)-admissible mappings introduced in ([14], S. Chandok, K. Tas, A. H. Ansari, Some fixed point results for TAC-type contractive mappings, the framework of b-metric spaces. To achieve this, we introduce the notion of (α, β) − S-admissible mappings and a new class of generalized (ψ, F)-contra...

Article to be published in Nonlinear Functional Analysis and Applications.
Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis,...

In this paper, we introduce a trifunction split equilibrium problem using a generalized relaxed α-monotonicity in the framework of p-uniformly convex and uniformly smooth Banach spaces. We develop an iterative algorithm for approximating a common solution of split equilibrium problem and fixed point problem for finite family of Bregman quasi-nonexp...

In this article, we introduce a new mixed-type iterative algorithm for approximation of common fixed points of two multivalued almost contractive mappings and two multivalued
mappings satisfying condition (E) in hyperbolic spaces. We consider new concepts of weak w^2-stability and data dependence results involving two multivalued almost contractive...

In this article, motivated by the works of Ali Akbar and Elahe Shahrosvand [Split equality common null point problem for Bregman quasi-nonexpansive mappings, Filomat 32 (2018), no. 11, 3917-3932], Eskandani et al. [A hybrid extragradient method for solving pseudomonotone equilibrium problem using Bregman distance, J. Fixed Point Theory Appl. 20 (20...

The purpose of this paper is to re-establish the convergence, stability and data dependence results established by [2] and [3] by removing the strong assumptions imposed on the sequences which were used to obtain their results. In addition, we introduced a modified approach using the D-iterative method to solve a two-point second-order boundary val...

To be published in Studia Universitatis Babeş-Bolyai Mathematica.
In this paper, we study split null point problem in reflexive Banach spaces. Using the Bregman technique together with a modified inertial Halpern method, we approximate a solution of split null point problem. Also, we establish a strong convergence result for approximating the solut...

In this paper, we propose an iterative method for finding the common element of the set of fixed points of a Reich-Suzuki nonexpansive mappings and the set of solutions of the variational inequalities problems in the framework of Hilbert spaces. In addition, we establish convergence results for these proposed iterative methods under some mild condi...

In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solutions of split monotone variational inclusion problems which is also a fixed point problem of Bregman relatively nonexpansive mapping in $p$-uniformly convex Banach spaces which are also uniformly smooth. Moreover, our iterative met...

In this paper, we considered the split monotone variational inclusion problem which includes the split variational inclusion problem and split feasibility problem, to mention a few. We introduced a Halpern iterative method for approximating a common solution of split best proximity point and split monotone variational inclusion problems with multip...

In this paper, we study split generalized mixed equilibrium problem and fixed point problem in real Hilbert spaces with a view to analyze an iterative method for approximating a common solution of split generalized mixed equilibrium problem and fixed point of an infinite family of an infinite family of quasi-nonexpansive mappings. The iterative alg...

In this paper, by employing a Bregman \textcolor{red}{distance} approach, we introduce a self-adaptive inertial extragradient method for solving a variational inequality problem involving a pseudo-monotone operator and the set of fixed point problem of a Bregman demigeneralized mapping in a reflexive Banach space. Using a Bregman distance approach,...

In this paper, we study the split equality convex minimization and fixed point problems for non-expansive semigroups in real Hilbert spaces. This problem is a natural extension of the convex minimization problem, fixed point problem for a nonexpansive semigroup mapping and split equality fixed point problem. We employ a shrinking projection method...

To be published in Nonlinear Functional Analysis and Application. In this paper, we present a modified (improved) generalized M-iteration with the inertial technique for three quasi-nonexpansive multivalued mappings in a real Hilbert space. In addition, we obtain a weak convergence result under suitable conditions and the strong convergence result...

The purpose of this paper is to introduce a new class of bilevel problem in the frame work of a real Hilbert space. In addition, we introduce an inertial iterative method with a regularization term and we establish the strong convergence of the resulting methods under certain conditions imposed on regularization parameters. Finally, we present some...

To be published in Journal of Nonlinear Functional Analysis. The purpose of this paper is to introduce a generalized inertial extrapolation method with regular-ization term for approximating the solutions of a monotone and Lipschitz variational inequality and fixed point problems in a real Hilbert space. In addition, we establish the strong converg...

In this paper, we study split common fixed point problems of Bregman demigeneralized and Bregman quasi-nonexpansive mappings in reflexive Banach spaces. Using the Bregman technique together with a Halpern iterative algorithm, we approximate a solution of split common fixed point problem and sum of two monotone operators in reflexive Banach spaces....

The research efforts of this paper is to present a new inertial relaxed Tseng extrapolation method with weaker conditions for approximating the solution of a variational inequality problem, where the underlying operator is only required to be pseudomonotone. The strongly pseudomonotonicity and inverse strongly monotonicity assumptions which the exi...

Article was published in Nonlinear Functional and Applications. In this paper, we present some fixed point results for a general class of nonexpansive mappings in the framework of Banach space and also proposed a new iterative scheme for approximating the fixed point of this class of mappings in the frame work of uniformly convex Banach spaces. Fur...

In this paper, we introduce a new type of a generalized split monotone variational inclusion problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a solution of generalized split monotone variational inclusion...

In this paper, we introduce an inertial forward-backward splitting method together with a viscosity iterative algorithm for approximating a common solution of a system of split monotone variational inclusion problem and fixed point problem of finite family of multivalued demicontractive mappings in Hilbert spaces. Under suitable conditions, we prov...

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 additi...

To be published in Nonlinear Functional Analysis and Applications.
In this paper, we propose a viscosity iterative algorithm for approximating a common solution of finite family of variational inequality problem and fixed point problem for finite family of multi-valued type-one demicontractive mappings in real Hilbert spaces. A strong convergence r...

Published in Nonlinear Functional Analysis and Application.
In this paper, we investigate a hybrid algorithm for finding zeros of the sum- of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in u...

In this paper, we propose a new modified relaxed inertial regularization method for finding a common solution of a generalized split feasibility problem, the zeros of sum of maximal monotone operators, and fixed point problem of two nonlinear mappings in real Hilbert spaces. We prove that the proposed method converges strongly to a minimum-norm sol...

In this paper, we present some fixed point results for a generalized class of nonexpansive mappings in the framework of uniformly convex hyper-bolic space and also propose a new iterative scheme for approximating the fixed point of this class of mappings in the framework of uniformly convex hyperbolic spaces. Furthermore, we establish some basic pr...

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of F-contraction introduced by Wardowski in ([22], D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-t...

In this paper, we investigate a shrinking algorithm for finding a solution of split monotone variational inclusion problem which is also a common fixed point problem of relatively nonexpansive mapping in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that i...

We consider the nonlinear diffusion equation with a perturbed convection term. The potential symmetries for the exact equation with respect to the second conservation law are classified. It is found that these exist only in the linear case. It is further shown that no nontrivial approximate potential symmetries of order one exists for the perturbed...

Published in Nonlinear Functional Analysis and Application. The concepts of new classes of mappings are introduced in the spaces which are more general space than the usual metric spaces. The obtained results are new and are extension of Banach contraction principle. The existence and uniqueness of common fixed points and fixed point results for th...

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 equ...

In this paper, we introduce a new three steps iteration process, prove that our newly proposed iterative scheme can be used to approximate the fixed point of a contractive-like mapping and establish some convergence results for our newly proposed iterative scheme generated by a mapping satisfying condition (E) in the framework of uniformly convex B...

In this paper, we introduce a new three steps iteration process, prove that our newly proposed iterative scheme can be used to approximate the fixed point of a contractive-like mapping and establish some convergence results for our newly proposed iterative scheme generated by a mapping satisfying condition (E) in the framework of uniformly convex B...

In this paper, we introduce a new class of monotone generalized nonexpansive mappings and we establish some weak and strong convergence theorem for a newly proposed iterative process in the frame work of an ordered Banach space. This class of mappings is wider than the class of nonexpansive mappings, mean nonexpansive mappings and mappings satisfyi...

The purpose of this work is to introduce the notion of a multivalued strictly (α, β)-admissible mappings and a multivalued (α, β)-Meir-Keeler contractions with respect to the partial Hausdorff metric Hp in the framework of partial metric spaces. In addition, we present fixed points and endpoints results for a multivalued (α, β)-Meir-Keeler contract...

Published in Nonlinear Functional Analysis and Applications.The goal of this paper is to introduce a modified Halpern iterative algorithm for approximating solutions of split monotone variational inclusion, variational inequality and fixed point problems of an infinite families of multi-valued type-one demicontractive mappings in the framework of r...

Published in Nonlinear Functional Analysis and Applications. The purpose of this paper is to present some sufficient conditions for the existence and uniqueness of solutions of the nonlinear Hammerstein integral equations and the two-point boundary value problems for nonlinear second-ordinary differential equations. To establish this, we introduce...

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 framework of G-metric spaces. Fixed point theorems for these class of mappings a...

Understanding how university students make sense of mathematics is always of concern to their lecturers. A group of lecturers at a South African university studied written responses of first year students to explore what mental conflicts arose during their students' formulations of solutions to assigned tasks. The mental conflicts as illustrated by...

## Projects

Project (1)