Ojen Narain

University of KwaZulu-Natal | ukzn · School of Mathematics, Statistics and Computer Science

In this paper, we propose an inertial iterative method for solving a common solution to the fixed point and mixed equilibrium problem in Hilbert spaces. We prove the sequence generated by the proposed algorithm strongly converges to an element in the solution set of mixed equilibrium problems of a pair of bi-function, which is also the solution to...

In order to solve variational inequality problems for which the cost operator is quasimonotone and Lipschitz continuous in real Hilbert spaces, we propose a new double inertial subgradient extragradient method. The new method involves double inertial extrapolation steps and a self-adaptive step size. The weak convergence result of our method is est...

In this paper, our main interest is to propose a viscosity iterative method for approximating solutions of variational inequality problems, resolvents of monotone operators and fixed points of ρ-demimetric map-pings with multiple output sets in Hadamard spaces. We prove a strong convergence result for approximating the solutions of the aforemention...

In this paper, the uniform eventual stability of nonlinear impulsive Caputo fractional differential equations with fixed moments of impulse is examined using the vector Lyapunov functions which is generalized by a class of piecewise continuous Lyapunov functions. Together with comparison results, sufficient conditions for the uniform eventual stabi...

The purpose of this article is to suggest a modified subgradient extragradient method that includes double inertial extrapolations and viscosity approach for finding the common solution of split equilibrium problem and fixed point problem. The strong convergence result of the suggested method is obtained under some standard assumptions on the contr...

In this article, we consider the AI-iteration process for approximating the fixed points of enriched contraction and enriched nonexpansive mappings. Firstly, we prove the strong convergence of the AI-iteration process to the fixed points of enriched contraction mappings. Furthermore, we present a numerical experiment to demonstrate the efficiency o...

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 solution of the aforementioned problems. It is worth mentioning that th...

In this research, we present a new relaxed intertial algorithm without viscosity for solving common solution of countable family of nonexpansive mappings in real Hilbert spaces. We obtain the strong convergence results of the proposed method under some wild conditions on the control parameters. We apply our main results to solve convex bilevel opti...

To be published in Nonlinear Functional Analysis and Applications. In this paper, we investigate a self adaptive accelerated method for solving split common fixed point problem for a finite family of firmly-nonexpansive type mappings (Type P) and monotone variational inclusion problem in p-uniformly convex and uniformly smooth Banach spaces. Using...

Published in Nonlinear Functional Analysis and Applications. In this research, we propose a new efficient iterative method for fixed point problem of generalized α-nonexpansive mappings. We show the weak and strong convergence analysis of the proposed method under some mild assumptions on the control parameters. We consider the application of the n...

Published in "Nonlinear Functional Analysis and Applications". In this paper, we propose an inertial method for solving a common solution to fixed point and Variational Inequality Problem in Hilbert spaces. Under some standard and suitable assumptions on the control parameters, we prove that the sequence generated by the proposed algorithm converge...

This study presents an interesting method based on Picard-Ishikwa fixed point iterative method to solve nonlinear third-order boundary value problems. We develop a sequence called Picrad-Ishikawa Green's iterative method and show that the sequence converges strongly to the fixed point of an integral operator. Our result improve many existing result...

Correction: The Journal of Analysis https://doi.org/10.1007/s41478-024-00756-x In this article the title was incorrectly given as ‘A modified inertial Tseng technique ofBilevel variational inequality problem withapplication toimage processing’ but should have been ‘A modified inertial Tseng technique of Bilevel variational inequality problem with a...

The purpose of this work is to introduce and study a new type of a relaxed extrapolation iterative method for approximating the solution of a split monotone inclusion problem in the framework of Hilbert spaces. More so, we establish a strong convergence theorem of the proposed iterative method under the assumption that the set-valued operator is ma...

To be published in Nonlinear Functional Analysis and Applications. The purpose of this paper is to introduce an iterative method for finding a common solution to fixed point problems and split generalized equilibrium problems of demi-metric mappings in real Hilbert spaces. We are motivated by the convergence properties of the proposed method and es...

The purpose of this paper is to introduce an iterative algorithm for approximating an element in the solution set of the common split feasibility problem for fixed points of demimetric mappings and equilibrium problem for monotone mapping in real Hilbert spaces. Motivated by self-adaptive step size method, we incorporate the inertial technique to a...

This article presents a modified Picard-S iterative method in hyperbolic spaces. The proposed iterative method is used to approximate the common fixed point two contractive-like mappings. We consider new concepts of data dependence and weak w 2-stability results of the proposed iterative scheme involving two contractive-like mappings in hyperbolic...

In this paper, we propose and study a Bilevel quasimonotone Variational Inequality Problem (BVIP) in the framework of Hilbert space. We introduce a new modified inertial iterative technique with self-adaptive step size for approximating a solution of the BVIP. In addition, we established a strong convergence result of the proposed iterative techniq...

This paper presents and examines a newly improved linear technique for solving the equilibrium problem of a pseudomonotone operator and the fixed point problem of a nonexpansive mapping within a real Hilbert space framework. The technique relies two modified mildly inertial methods and the subgradient extragradient approach. In addition, it can be...

In this paper, we propose and study a new modified Tseng inertial iterative technique for solving Bilevel quasimonotone Variational Inequality Problem (BVIP) in the framework of Hilbert spaces. In addition, we establish a strong convergence result of the proposed iterative technique under some mild assumptions, the proposed iterative technique does...

In order to approximate the common solution of quasi-nonexpansive fixed point and pseudo-monotone variational inequality problems in real Hilbert spaces, this paper presented three new modified sub-gradient extragradient-type methods. Our algorithms incorporated viscosity terms and double inertial extrapolations to ensure strong convergence and to...

In this paper, we introduce and study a viscous-type extrapolation algorithm for finding a solution of the variational inequality problem and a fixed point constraint of quasi-nonexpansive mappings under the scope of real Hilbert spaces when the underlying cost operator is quasi-monotone. The method involves inertial viscosity approximation and a c...

This article proposes an iteration algorithm with double inertial extrapolation steps for approximating a common solution of split equilibrium problem, fixed point problem and variational inequity problem in the framework of Hilbert spaces. Unlike several existing methods, our algorithm is designed such that its implementation does not require the...

In this paper, we investigate a self adaptive accelerated method for solving split common fixed point problem for a finite family of firmly-nonexpansive type mappings (Type P) and monotone variational inclusion problem in p-uniformly convex and uniformly smooth Banach spaces. Using a modified Halpern method together with an inertial extrapolation m...

Published in Nonlinear Functional Analysis and Applications. In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertia...

To be published in Nonlinear Functional Analysis and Applications. In this paper we study the problem of finding a common solution to a fixed point problem involving a finite family of ρ-demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial techn...

Published in Nonlinear Functional Analysis and Applications. In this article, we study the Picard-Ishikawa iterative method for approximating the fixed point of generalized α-Reich-suzuki nonexpanisive mappings. The weak and strong convergence theorems of the considered method are established with mild assumptions. Numerical example is provided to...

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...

The purpose of this article is to study A∗ iterative algorithm in hyperbolic space. We prove the weak w^2-stability, data dependence and convergence results of the proposed iterative algorithm for contractive-like mappings in hyperbolic spaces. Furthermore, we study several strong and �-convergence analysis for fixed points of generalized Reich–Suz...

In this paper, we introduce an inertial forward-backward splitting method together with a Halpern iterative algorithm for approximating a common solution of a finite family of split minimization problem involving two proper, lower semicontinuous and convex functions and fixed point problem of a nonex-pansive mapping in real Hilbert spaces. Under su...

In this paper, we introduce and study a modified inertial subgradient extragradient iterative method for solving bilevel split quasimonotone variational inequality problems in the framework of real Hilbert spaces. The method involves strongly monotone operators and quasimonotone operators as the cost operators. In addition, we obtain a strong conve...

In this article, the problem of solving a strongly monotone variational inequality problem over the solution set of a monotone inclusion problem in the setting of real Hilbert spaces is considered. To solve this problem, two methods, which are improvements and modifications of the Tseng splitting method, and projection and contraction methods, are...

In this article, we consider the problem of approximating the common solution of monotone inclusions and demicontraction fixed point problems. Firstly, we present Tseng splitting method which incorporates the viscosity technique, new self-adaptive step size and double inertial extrapolations techniques for approximating the solution of the problem...

In this paper, we introduce a Halpern iteration process for computing the common solution of split generalized equilibrium problem and fixed points of a countable family of Bregman W-mappings with multiple output sets in reflexive Banach spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems unde...

In this article, we introduce the hyperbolic space version of a faster iterative algorithm. The proposed iterative algorithm is used to approximate the common fixed point of three multi-valued almost contraction mappings and three multi-valued mappings satisfying condition (E) in hyperbolic spaces. The concepts weak w 2-stability involving three mu...

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...

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 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...

In this paper, we study an iterative algorithm that is based on inertial projection and contraction methods for solving bilevel quasimonotone variational inequality problems in the framework of real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on adaptive stepsizes conditions without prior knowledg...

In this article, we study the split equality problem involving nonexpansive semigroup and convex minimization problem. Using a Halpern iterative algorithm, we establish a strong convergence result for approximating a common solution of the aforementioned problems. The iterative algorithm introduced in this paper is designed in such a way that it do...

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 article, we introduce an inertial-type algorithm that combines the extragradient subgradient method, the projection contraction method, and the viscosity method. The proposed method is used for solving quasimonotone variational inequality problems in infinite dimensional real Hilbert spaces such that it does not depend on the Lipschitz cons...

In this article, we propose the modified AH iteration process in Hyperbolic spaces to approximate the fixed points of mappings enriched with condition (E). The data dependence result of the proposed iteration process is studied for almost contraction mappings. Further, we obtain several new strong and-convergence results of the proposed iteration a...

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...

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...

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 pseudocontrac...

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 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...

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...

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...