A modified proximal point algorithm involving nearly asymptotically quasi-nonexpansive mappings

Abstract

Abstract In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate the common element of the set of solutions of convex minimization problems and the fixed points of two nearly asymptotically quasi-nonexpansive mappings in the framework of CAT ( 0 ) $\operatorname{CAT}(0)$ spaces. We also prove the Δ-convergence of the proposed algorithm. We also provide an application and numerical result based on our proposed algorithm as well as the computational result by comparing our modified iteration with previously known Sahu’s modified iteration.

Keywords

• CAT ( 0 ) $\operatorname{CAT}(0)$ space
• Nearly asymptotically quasi-nonexpansive mappings
• Δ-convergence