Strong convergence for total asymptotically pseudocontractive semigroups in Banach spaces

Jing Quan,Xiongrui Wang

doi:10.1186/1687-1812-2012-216

Abstract

In this article, the demiclosedness principle for total asymptotically pseudocontractions in Banach spaces is established. The strong convergence to a common fixed point of total asymptotically pseudocontractive semigroups in Banach spaces is established based on the demiclosedness principle, the generalized projective operator, and the hybrid method. The main results presented in this article extend and improve the corresponding results of many authors. MSC:47H05, 47H09, 49M05.

Highlights

1 Introduction Throughout this article, we assume that E is a real Banach space with the norm ·, E∗ is the dual space of E; ·, · is the duality pairing between E and E∗; C is a nonempty closed convex subset of E; N and R+ denote the natural number set and the set of nonnegative real numbers, respectively
Qin et al [ ] have introduced total asymptotically pseudocontractive mappings and proved a weak convergence theorem of fixed points for total asymptotically pseudocontractive mappings in Hilbert spaces
Qin[ ] introduced the class of total asymptotically pseudocontractive mappings in Hilbert spaces and established a weak convergence theorem of fixed points

Summary

Introduction

Throughout this article, we assume that E is a real Banach space with the norm · , E∗ is the dual space of E; ·, · is the duality pairing between E and E∗; C is a nonempty closed convex subset of E; N and R+ denote the natural number set and the set of nonnegative real numbers, respectively. Qin et al [ ] have introduced total asymptotically pseudocontractive mappings and proved a weak convergence theorem of fixed points for total asymptotically pseudocontractive mappings in Hilbert spaces. One-parameter family T := {T(t) : t ≥ } of mappings from C into itself is said to be an asymptotically pseudocontractive semigroup on C, if the conditions (a), (b), (c) in Definition .

Objectives

Results

Conclusion