On ultimately nonexpansive semigroups

Strong Convergence Theorems for Asymptotically Nonexpansive Mappings and Asymptotically Nonexpansive Semigroups

A point x ∈ C is a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T ; that is, F(T)= {x ∈ C : Tx = x}. Also, recall that a family S= {T(s) | 0≤ s <∞} of mappings from C into itself is called an asymptotically nonexpansive semigroup on C if it satisfies the following conditions: (i) T(0)x = x for all x ∈ C; (ii) T(s+ t)= T(s)T(t) for all s, t ≥ 0; (iii) there exists ...

Hybrid Algorithms of Nonexpansive Semigroups for Variational Inequalities

Copyright q 2012 Peixia Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Two hybrid algorithms for the variational inequalities over the common fixed points set of nonexpansive semigroups are presented. Strong convergen...

Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals

The general iterative methods for nonexpansive semigroups in Banach spaces

Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E∗. Let S {T s : 0 ≤ s < ∞} be a nonexpansive semigroup on E such that Fix S : ⋂t≥0Fix T t / ∅, and f is a contraction on E with coefficient 0 < α < 1. Let F be δ-strongly accretive and λ-strictly pseudocontractive with δ λ > 1 and γ a positive real number such that γ < 1/α 1 − √ 1 − δ...

Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups

Throughout this paper, letH be a real Hilbert space with inner product 〈·,·〉 and ‖ · ‖. We use xn⇀ x to indicate that the sequence {xn} converges weakly to x. Similarly, xn → x will symbolize strong convergence. we denote by N and R+ the sets of nonnegative integers and nonnegative real numbers, respectively. let C be a closed convex subset of a Hilbert space H , and Let T : C → C be a nonexpan...