Multiple-set split feasibility problems for κ-asymptotically strictly pseudo-nonspreading mappings in Hilbert spaces

Jing Quan,Shih-Sen Chang

doi:10.1186/1029-242x-2014-69

Abstract

Some weak and strong convergence theorems for solving multiple-set split feasibility problems for κ-asymptotically strictly pseudo-nonspreading mappings in infinite-dimensional Hilbert spaces are proved. The results presented in the paper extend and improve the corresponding results of Xu (Inverse Probl. 22(6):2021-2034, 2006), Osilike and Isiogugu (Nonlinear Anal. 74:1814-1822, 2011), Chang et al. (Abstr. Appl. Anal. 2012:491760, 2012), and others.

Highlights

Throughout this article, we always assume that H, H are real Hilbert spaces; ‘→’ and ‘ ’
The split feasibility problem (SFP) in finite dimensional spaces was first introduced by Censor and Elfving [ ] for modeling inverse problems
Definition . [ ] Let H be a real Hilbert space, we say that the mapping T : D(T) ⊂ H → H is a κ-asymptotically strict pseudo-contraction if there exists a constant κ ∈ [, ) and a sequence {kn} ⊂ [, ∞) with kn → (n → ∞) such that

Summary

Introduction

Throughout this article, we always assume that H , H are real Hilbert spaces; ‘→’ and ‘ ’denote strong and weak convergence, respectively.The split feasibility problem (SFP) in finite dimensional spaces was first introduced by Censor and Elfving [ ] for modeling inverse problems. A mapping T : D(T) ⊂ H → H is said to be κ-strictly pseudo-nonspreading if there exists κ ∈ [ , ) such that Chang et al [ ] studied the multiple-set split feasibility problem for an asymptotically strict pseudo-contraction in the framework of infinite-dimensional Hilbert spaces.

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Results

Conclusion