Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings

Abstract

In this paper, weak and strong convergence theorems are established for a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. Mann-type and Ishikawa -type iterations are included by the new iterative scheme. The results obtained in this paper extend and improve the recent ones announced by Xu and Noor, Glowinski and Le Tallec, Noor, Ishikawa, and many others.  2005 Elsevier Inc. All rights reserved.

Convergence analysis of new modified iterative approximating processes for two finite families of total asymptotically nonexpansive nonself mappings in hyperbolic spaces

“…The results presented in the paper extend and improve some recent results given in [4,5,14,19,20,24,27,29,30,33]. Some special cases are listed as follows.…”

“…Moreover, Sahin and Basarir [20] considered a unified treatment regarding iterative process for total asymptotically nonexpansive mapping in hyperbolic spaces. For more detail, refer to [19,24] and the references therein. Example 1.4.…”

Fixed point theorems of finite family with errors for asymptotically quasi-nonexpansive mappings in convex metric spaces

“…The main result of this paper is also, an extension and improvement of the well known corresponding results in [1] - [5], [7,8], [11] - [13], [15] - [18] and [20].…”

“…In 2004, Cho et al [4] extended the work of Xu and Noor [20] to the three step iterative scheme with errors in Banach space and gave weak and strong convergence theorems for asymptotically nonexpansive mappings in a Banach space. Moreover, Suantai [18] gave weak and strong convergence theorems for a new three step iterative scheme of asymptotically nonexpansive mappings. More recently, Plubtieng et al [16] introduced three step iterative scheme with errors for three asymptotically nonexpansive mapping and established strong convergence of this scheme to common fixed point of three asymptotically nonexpansive mappings.…”

Weak convergence theorem for the three-step iterations of non-Lipschitzian nonself mappings in Banach spaces

“…Fixed-point iterations process for nonexpansive and asymptotically nonexpansive mappings in Banach spaces have been studied extensively by various authors [1][2][3][4][5][6][7][8][9][10][11][12][13]. In 1991, Schu [4] considered the following modified Mann iteration process for an asymptotically nonexpansive map T on C and a sequence {a n } in [0, 1]:…”