Solving Split Equality Fixed Point of Nonexpansive Semigroup and split equality minimization Problems in real Hilbert Space

Hammed Anuoluwapo Abass\(^{a,b,c*}\), Ojen Kumar Narain\(^a\)

\(^a\)School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa.

\(^b\)DSI-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS).

\(^c\)Department of Mathematics and Applied Mathematics, Sefako Makgato Health Science University , P.O. Box 94, Pretoria 0204, South Africa.

Correspondence should be addressed to: : AbassH@ukzn.ac.za, hammedabass548@gmail.com

Copyright © 2023 Hammed Anuoluwapo Abassa, Ojen Kumar Narain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 31 October 2022; Accepted: 29 January 2023; Published Online: 08 June 2023.

Abstract

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 does not require the knowledge of the operator norm. We display a numerical example to show the relevance of our result. Our result complements and extends some related results in literature

Keywords:

Split equality minimization problem; semigroup nonexpansive; iterative scheme; Fixed point problem.