Weak and strong convergence theorems for finite families of asymptotically nonexpansive mappings in Banach spaces (Q874951)

The authors prove the following theorems in real uniformly convex Banach space \(E\). (1) A~weak convergence theorem for finite families of asymptotically nonexpansive mappings in the case where the dual space \(E^*\) of \(E\) satisfies the Kadec-Klee property. (2) A strong convergence theorem of one member of the family of asymptotically nonexpansive maps \(\{T_i\}\) satisfies a condition weak than semicompactness. These theorems generalize and improve results of \textit{S. H. Khan} and \textit{H. Fukhar-ud-din} [Nonlinear Anal., Theory Methods Appl. 61, No. 8 (A), 1295--1301 (2005; Zbl 1086.47050)], \textit{N. Shahzad} [Nonlinear Anal., Theory Methods Appl. 61, No. 6 (A), 1031--1039 (2005; Zbl 1089.47058)] and \textit{N. Shahzad} and \textit{R. Al-Dubiban} [Georgian Math. J. 13, No. 3, 529--537 (2006; Zbl 1136.47049)].