Proximal point algorithms involving Cesàro type mean of total asymptotically nonexpansive mappings in CAT(0) spaces

Abstract

In this paper, we study the proximal point algorithm proposed by Chang et al. [S.S. Chang, C.F. Wen and J. C. Yao, Proximal point algorithms involving Ces aro type mean of asymptotically nonexpansive mappings in CAT(0) spaces, J. Nonlinear Sci. Appl. 9 (2016), 4317-4328.] for total asymptotically nonexpansive mappings in CAT(0) spaces. We demonstrate the Δ-convergence and strong convergence to a common element of the set of minimizers of a convex function and the set of fixed points of the Cesàro type mean of total asymptotically nonexpansive mapping in CAT(0) space.