Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Abstract

In this paper, we propose and study a multi-step iterative algorithm that comprises of a finite family of asymptotically $ k_i $-strictly pseudocontractive mappings with respect to $ p, $ and a $ p $-resolvent operator associated with a proper convex and lower semicontinuous function in a $ p $-uniformly convex metric space. Also, we establish the $ \Delta $-convergence of the proposed algorithm to a common fixed point of finite family of asymptotically $ k_i $-strictly pseudocontractive mappings which is also a minimizer of a proper convex and lower semicontinuous function. Furthermore, nontrivial numerical examples of our algorithm are given to show its applicability. Our results complement a host of recent results in literature.