𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Approximation of common fixed points for a countable family of relatively nonexpansive mappings in a Banach space and applications

✍ Scribed by Somyot Plubtieng; Kasamsuk Ungchittrakool

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
767 KB
Volume
72
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we prove a strong convergence theorem by the hybrid method for a countable family of relatively nonexpansive mappings in a Banach space. We also establish a new control condition for the sequence of mappings {T n } which is weaker than the control condition in Lemma 3.1 of Aoyama et al. [K. Aoyama, Y. Kimura, W. Takahashi and M. Toyoda, Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007) 2350-2360]. Moreover, we apply our results for finding a common fixed point of two relatively nonexpansive mappings in a Banach space and an element of the set of solutions of an equilibrium problem in a Banach space, respectively. Our results are applicable to a wide class of mappings.

πŸ“œ SIMILAR VOLUMES

Approximation of common fixed points of
Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces
✍ Yeol Je Cho; Shin Min Kang; Xiaolong Qin πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 261 KB

Let C be a closed convex subset of a real uniformly smooth and strictly convex Banach space E. Consider the following iterative algorithm given by where f is a contraction on C and W n is a mapping generated by an infinite family of nonexpansive mappings {T i } ∞ i=1 . Assume that the set of common

Iterative methods for common fixed point
Iterative methods for common fixed points for a countable family of nonexpansive mappings in uniformly convex spaces
✍ C.E. Chidume; C.O. Chidume πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 679 KB

Let E be a uniformly convex real Banach space with a uniformly GÒteaux differentiable norm. Let K be a closed, convex and nonempty subset of E. Let {T i } ∞ i=1 be a family of nonexpansive self-mappings of K . For arbitrary fixed δ ∈ (0, 1), define a family of nonexpansive maps , where {α n } and {