Convergence analysis for minimization problem and fixed point problem in p-uniformly convex metric spaces

Abstract

In this paper, we study the strong convergence of a Mann-type proximal point algorithm to a minimizer of a proper convex and lower semicontinuous function in a complete p-uniformly convex metric space. Also, we introduce and study an iterative algorithm involving a finite family of generalized strictly pseudononspreading mappings in p-uniformly convex metric space. Furthermore, we prove the demicloseness principle for this class of mappings and obtained a Δ-convergence of our proposed algorithm to a common fixed point of finite family of these mappings in the setting of a complete p-uniformly convex metric space.