The Split Feasibility Problems for Countable Families of Asymptotically Strict Pseudocontractions

Wei-Qi Deng

doi:10.1155/2013/817943

Abstract

An up-to-date algorithm for solving the split feasibility problem for countable families of asymptotically strict pseudocontractions is introduced in the framework of Hilbert spaces. Our results greatly improve and extend those of other authors whose related research studies are restricted to the situation of at most finitely many such mappings.

Highlights

The split feasibility problem (SFP) in finite dimensional spaces was first introduced by Censor and Elfving [1] for modeling inverse problems which arise from phase retrievals and in medical image reconstruction [2]
It has been found that the SFP can be used in various disciplines such as image restoration, computer tomograph, and radiation therapy treatment planning [3,4,5]
The purpose of this paper is to introduce and study the following multiple-set split feasibility problem for an infinite family of asymptotically strict pseudocontractions (MSSFP) in the framework of infinite-dimensional Hilbert spaces

Summary

Introduction

The split feasibility problem (SFP) in finite dimensional spaces was first introduced by Censor and Elfving [1] for modeling inverse problems which arise from phase retrievals and in medical image reconstruction [2]. The purpose of this paper is to introduce and study the following multiple-set split feasibility problem for an infinite family of asymptotically strict pseudocontractions (MSSFP) in the framework of infinite-dimensional Hilbert spaces. A Banach space E is said to satisfy Opial’s condition, if for any sequence {xn} in E, xn ⇀ x∗ implies that lim inf n→∞

Objectives

Results

Conclusion