A multi-step approximant for fixed point problem and convex optimization problem in Hadamard spaces

Abstract

The purpose of this paper is to propose and analyze a multi-step iterative sequence to solve a convex optimization problem and a fixed point problem in an Hadamard space. We aim to establish strong and $$ \triangle $$ -convergence results of the proposed iterative sequence by employing suitable conditions on the control parameters and the structural properties of the underlying space. As a consequence, we compute an optimal solution for a minimizer of proper convex lower semicontinuous function and a common fixed point of a finite family of total asymptotically quasi-nonexpansive mappings in Hadamard spaces. Our results can be viewed as an extension and generalization of various corresponding results in the existing literature.