Iterative approximation to common fixed points of a countable family of nonexpansive mappings

作者：Song Yisheng^*

来源：APPLICABLE ANALYSIS, 2007, 86(11): 1329-1337.

DOI：10.1080/00036810701556144

• uniformly asymptotically regular sequence
• viscosity approximation methods
• weakly continuous duality mapping

We proved several strong convergence results by using the conception of a uniformly asymptotically regular sequence {T-n} of nonexpansive mappings in a reflexive Banach space which admits a weakly continuous duality mapping J(phi)(l(l') (l < p < infinity) has a weakly continuous duality map with gauge phi(t)=t(p-1). The results presented develop and complement the corresponding ones by Song, Y. and Chen, R., 2007 [Iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive Banach spaces. Nonlinear Analysis, 66, 591-603], Song, Y., Chen, R. and Zhou, H., 2007 [Viscosity approximation methods for nonexpansive mapping sequences in Banach spaces. Nonlinear Analysis, 66, 1016-1024] and O'Hara, J.G., Pillay, P. and Xu, H.K., 2006 [Iterative approaches to convex feasibility problem in Banach Space. Nonlinear Analysis, 64, 2022-2042], O'Hara, J.G., Pillay, P. and Xu, H.K., 2003 [Iterative approaches to fineding nearest common fixed point of nonexpansive mappings in Hilbert spaces. Nonlinear Analysis, 54, 1417-1426] and Jung, J.S., 2005 [Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces. Journal of Mathematical Analysis and Applications, 302, 509-520] and many other existing literatures.

• 出版日期2007-11
• 单位河南师范大学