Strong convergence of Monotone CQ algorithm for relatively nonexpansive mappings

Abstract

X. Qin and Y. Su proved a strong convergence theorems of modified Ishikawa iteration by CQ method for relatively nonexpansive mappings in a Banach space [Xiaolong Qin, Yongfu Su, Nonlinear Anal. 67 (2007), no. 6, 1958-1965]. The result of this paper extends and improves the result of X. Qin and Y. Su in the two respects: (1). By using the monotone CQ method to modify the CQ method, so that the new method of proof is used. (2). Relax the restriction on $T$ from uniformly continuous to continuous. The result of this paper also extends and improves the recent ones announced by Nakajo, Takahashi, Kim, Martinez-Yanes, Xu and some others.