an:05720172
Zbl 1226.47080
Klin-Eam, Chakkrid; Suantai, Suthep
Strong convergence of composite iterative schemes for a countable family of nonexpansive mappings in Banach spaces
EN
Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 2, 431-439 (2010).
0362-546X
2010
j
47J25 47H06 47H09 47H10
viscosity approximation; strong convergence; countable family nonexpansive mappings; composite iterative schemes; fixed points; accretive operator
Summary: We propose a new modified viscosity approximation method for approximating common fixed points for a countable family of nonexpansive mappings in a Banach space. We prove strong convergence theorems for a countable family nonexpansive mappings in a reflexive Banach space with uniformly GĂ˘teaux differentiable norm under some control conditions. These results improve and extend the results of \textit{J. S. Jung} [Fixed Point Theory Appl. 2008, Article ID 167535 (2008; Zbl 1203.47053)]. Further, we apply our result to the problem of finding a zero of an accretive operator and extend the results of \textit{T.-H. Kim} and \textit{H.-K. Xu} [Nonlinear Anal., Theory Methods Appl. 61, No.~1--2, A, 51--60 (2005; Zbl 1091.47055)], \textit{L.-C. Ceng}, \textit{A. R. Khan}, \textit{Q. H. Ansari} and \textit{J.-C. Yao} [ibid. 70, No.~5, A, 1830--1840 (2009; Zbl 1226.47069)] and \textit{R.-D. Chen} and \textit{Z.-C. Zhu} [ibid. 69, No.~4, A, 1356--1363 (2008; Zbl 1196.47045)].
1226.47069; 1203.47053; 1091.47055; 1196.47045