Olawale Kazeem Oyewole

Bio: Olawale Kazeem Oyewole is an academic researcher from University of KwaZulu-Natal. The author has contributed to research in topics: Fixed point & Mathematics. The author has an hindex of 5, co-authored 20 publications receiving 57 citations. Previous affiliations of Olawale Kazeem Oyewole include DST Systems.

A strong convergence algorithm for a fixed point constrained split null point problem

Abstract: In this paper, we introduce a new algorithm with self adaptive step-size for finding a common solution of a split feasibility problem and a fixed point problem in real Hilbert spaces. Motivated by the self adaptive step-size method, we incorporate the self adaptive step-size to overcome the difficulty of having to compute the operator norm in the proposed method. Under standard and mild assumption on the control sequences, we establish the strong convergence of the algorithm, obtain a common element in the solution set of a split feasibility problem for sum of two monotone operators and fixed point problem of a demimetric mapping. Numerical examples are presented to illustrate the performance and the behavior of our method. Our result extends, improves and unifies other results in the literature.

On Mixed Equilibrium Problems in Hadamard Spaces

Abstract: The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a - convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.

An extragradient algorithm for split generalized equilibrium problem and the set of fixed points of quasi-$\phi $-nonexpansive mappings in Banach spaces

Abstract: In this paper, we study the problem of finding a common solution to split generalized mixed equilibrium problem and fixed point problem for quasi-$% \phi $-nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach space $E_1$ and a smooth, strictly convex, and reflexive Banach space $% E_2$. An iterative algorithm with Armijo linesearch rule for solving the problem is presented and its strong convergence theorem is established. The convergence result is obtained without using the hybrid method which is mostly used when strong convergence is desired. Finally, numerical experiments are presented to demonstrate the practicability, efficiency, and performance of our algorithm in comparison with other existing algorithms in the literature. Our results extend and improve many recent results in this direction.

A new efficient algorithm for finding common fixed points of multivalued demicontractive mappings and solutions of split generalized equilibrium problems in Hilbert spaces

Abstract: The purpose of this article is to present a new iterative technique for approximating solutions of split generalized equilibrium problem and common fixed points of multivalued demicontractive mappi...

Inertial approximation method for split variational inclusion problem in Banach spaces

Abstract: In this paper, we introduce a new iterative algorithm of inertial form for approximating the solution of Split Variational Inclusion Problem (SVIP) involving accrective operators in Banach space Motivated by the inertial technique, we incorporate the inertial term to accelerate the convergence of the proposed method Under standard and mild assumption of monotonicity of the SVIP associated mappings, we establish the weak convergence of the sequence generated by our algorithm Some applications and numerical example are presented to illustrate the performance of our method as well as comparing it with the non-inertial version

An inertial method for solving generalized split feasibility problems over the solution set of monotone variational inclusions

Abstract: In this paper, we propose a new inertial extrapolation method for solving the generalized split feasibility problems over the solution set of monotone variational inclusion problems in real Hilbert...

An iterative algorithm for solving variational inequality, generalized mixed equilibrium, convex minimization and zeros problems for a class of nonexpansive-type mappings

Abstract: In this paper, we study a classical monotone and Lipschitz continuous variational inequality and fixed point problems defined on a level set of a convex function in the framework of Hilbert spaces. First, we introduce a new iterative scheme which combines the inertial subgradient extragradient method with viscosity technique and with self-adaptive stepsize. Unlike in many existing subgradient extragradient techniques in literature, the two projections of our proposed algorithm are made onto some half-spaces. Furthermore, we prove a strong convergence theorem for approximating a common solution of the variational inequality and fixed point of an infinite family of nonexpansive mappings under some mild conditions. The main advantages of our method are: the self-adaptive stepsize which avoids the need to know a priori the Lipschitz constant of the associated monotone operator, the two projections made onto some half-spaces, the strong convergence and the inertial technique employed which accelerates convergence rate of the algorithm. Second, we apply our theorem to solve generalised mixed equilibrium problem, zero point problems and convex minimization problem. Finally, we present some numerical examples to demonstrate the efficiency of our algorithm in comparison with other existing methods in literature. Our results improve and extend several existing works in the current literature in this direction.

A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

Abstract: In this paper, we present a new modified self-adaptive inertial subgradient extragradient algorithm in which the two projections are made onto some half spaces Moreover, under mild conditions, we obtain a strong convergence of the sequence generated by our proposed algorithm for approximating a common solution of variational inequality problem and common fixed point of a finite family of demicontractive mappings in a real Hilbert space The main advantages of our algorithm are: strong convergence result obtained without prior knowledge of the Lipschitz constant of the related monotone operator, the two projections made onto some half-spaces and the inertial technique which speeds up rate of convergence Finally, we present an application and a numerical example to illustrate the usefulness and applicability of our algorithm