Δ-convergence and w-convergence of the modified Mann iteration for a family of asymptotically nonexpansive type mappings in complete CAT(0) spaces

摘要

In this paper, we show ?-convergence and w-convergence (in the sense of AhmadiKakavandi and Amini [2]) of modified Mann iterationxn+1 = αnP yn ⊕ (1 ? αn)TnnP yn; d(yn; xn) ≤ en; x0 2 C;to a common fixed point of the sequence (Tn) of asymptotically nonexpansive type selfmappings ona closed and convex subset C of a complete CAT(0) space X, where (αn) ? [0; 1], (en) ? R+ andP is the nearest point projection on C. Our results extend the results in [16, 21] in the setting ofcomplete CAT(0) spaces.