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

In this paper, a new modified proximal point algorithm involving fixed point of Cesaro type mean of asymptotically nonexpansive mappings in CAT(0) spaces is proposed. We also introduce a new iterative scheme. Under suitable conditions, the ∆-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 Cesaro type mean of asymptotically nonexpansive mapping in CAT(0) space are proved. The results presented in the paper are new.