CONVERGENCE OF IMPLICIT ITERATION PROCESS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES
Yuying Zhou, Shih-sen Chang · Numerical Functional Analysis and Optimization · 2002
The purpose of this paper is to study the weak and strong convergence of implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Refs. [1] Bauschke, H.H. 1996. The Approximation of Fixed Points of Compositions of Nonexpansive Mappings in Hilbert Space. J. Math. Anal. Appl., 202: 150–159. [Crossref], [Web of Science ®] , [Google Scholar], 5-7 Halpern, B. 1967. Fixed Points of Nonexpansive Maps. Bull. Amer. Math. Soc., 73: 957–961. Lions, P.L. 1977. Approximation de Points Fixes de Contractions. C.R. Acad. Sci. Paris, er. A, 284: 1357–1359. Reich, S. 1980. Strong Convergence Theorems for Resolvents of Accretive Operators in Banach Spaces. J. Math. Anal. Appl., 75: 287–292. , 10-11 Wittmann, R. 1992. Approximation of Fixed Points of Nonexpansive Mappings. Arch. Math., 58: 486–491. Xu, H.K. and Ori, R.G. 2001. An Implicit Iterative Process for Nonexpansive Mappings. Numer. Funct. Anal. and Optimiz., 22(5): 767–773. .