Δ-convergence for proximal point algorithm and fixed point problem in CAT(0) spaces

Abstract

Abstract In this paper, we prove the Δ-convergence of a modified proximal point algorithm for common fixed points in a CAT(0) space for different classes of generalized nonexpansive mappings including a total asymptotically nonexpansive mapping, a multivalued mapping, and a minimizer of a convex function. The results in this paper generalize the corresponding results given by some authors. Moreover, numerical example is given to illustrate and show the Δ-convergence of the proposed algorithm for supporting our result.

Keywords

• Proximal point algorithm
• Total asymptotically nonexpansive mapping
• Nonexpansive multivalued mapping
• Δ-convergence