THEOREMS OF THE MINIMIZATION PROBLEM AND FIXED POINT PROBLEM OF TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN CAT(0) SPACES

JIRAPORN  LIMPRAYOON

THEOREMS OF THE MINIMIZATION PROBLEM AND FIXED POINT PROBLEM OF TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN CAT(0) SPACES

Authors

JIRAPORN LIMPRAYOON Department of Mathematics, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand.

Keywords:

minimization problem, fixed point problem, total asymptotically nonexpansive mapping, convergence theorem, CAT(0) space

Abstract

In this paper, we propose an iterative algorithm designed to address the minimization and fixed point problems associated with total asymptotically nonexpansive mappings in CAT(0) spaces. We establish strong convergence theorems and △-convergence theorems for solving these problems. Furthermore, we apply the key findings to solve the equilibrium problem in CAT(0) spaces.