Abstract
Motivated by the method of Xu (2006) and Matsushita and Takahashi (2008), we characterize the set of all common fixed points of a family of nonexpansive mappings by the notion of Mosco convergence and prove strong convergence theorems for nonexpansive mappings and semigroups in a uniformly convex Banach space.
Highlights
Let C be a nonempty bounded closed convex subset of a Banach space and T : C → C a nonexpansive mapping; that is, T satisfies T x − T y ≤ x − y for any x, y ∈ C, and consider approximating a fixed point of T
Let us focus on the following methods generating an approximating sequence to a fixed point of a nonexpansive mapping
Throughout this paper, we denote by E a real Banach space with norm ·
Summary
Let C be a nonempty bounded closed convex subset of a Banach space and T : C → C a nonexpansive mapping; that is, T satisfies T x − T y ≤ x − y for any x, y ∈ C, and consider approximating a fixed point of T. This problem has been investigated by many researchers and various types of strong convergent algorithm have been established. In this paper, motivated by these results, we characterize the set of all common fixed points of a family of nonexpansive mappings by the notion of Mosco convergence and prove strong convergence theorems for nonexpansive mappings and semigroups in a uniformly convex Banach space
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