On Halpern's Proximal Point Algorithm in p-Uniformly Convex Metric Spaces

Abstract

The main purpose of this paper is to introduce a Halpern-type proximal point algorithm, comprising a nonexpansive mapping and a finite composition of p-resolvent mappings associated with proper convex and lower semicontinuous functions. A strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a nonexpansive mapping is established in a complete p-uniformly convex metric space. Also, numerical examples of the proposed algorithm in nonlinear settings are given to illustrate the applicability of the obtained results.