Proximal Point Algorithms Involving Cesàro Type Mean of Asymptotically Nonexpansive Mappings in CAT(0) Spaces
Shih-sen Chang, Ching‐Feng Wen, Jen‐Chih Yao · The Journal of Nonlinear Sciences and Applications · 2016
In this paper, a new modified proximal point algorithm involving fixed point of Cesàro type mean of asymptotically nonexpansive mappings in CAT(0) spaces is proposed. We also introduce a new iterative scheme. Under suitable conditions, the \(\Delta\)-convergence and the 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 asymptotically nonexpansive mapping in CAT(0) space are proved. The results presented in the paper are new.