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

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.