Strong Convergence of Multi-step Iterations with Errors for a Family of Finite Non-Lipschitzian Mappings

S. Plubtieng, I. Inchan

Abstract

In this paper, we established strong convergence theorems for a multi-step iterative scheme with errors for finite mappings of asymptotically nonexpansive in the intermediate sense in Banace spaces. Our results extend and improve the recent ones announced by Plubtieng andWangkeeree [ Strong convergence theorems for multi-step iterations with errors in Banach spaces, J. Math. Anal. Appl. 321 (2006) 10-23], Cho, Zhou and Guo [Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Computers Math. Applic. 47(4/5), 707-717, (2004)], and many others.