On the zero point problem of monotone operators in Hadamard spaces

Abstract

In this paper, by using products of finitely many resolvents of monotone operators, we propose an iterative algorithm for finding a common zero of a finite family of monotone operators and a common fixed point of an infinitely countable family of nonexpansive mappings in Hadamard spaces. We derive the strong convergence of the proposed algorithm under appropriate conditions. A common fixed point of an infinitely countable family of quasi-nonexpansive mappings and a common zero of a finite family of monotone operators are also approximated in reflexive Hadamard spaces. In addition, we define a norm on X◇ := spanX∗ and give an application of this norm, where X is an Hadamard space with dual space X∗. A numerical example to solve a nonconvex optimization problem will be exhibited in an Hadamard space to support our main results.