General split equality problems in Hilbert spaces

Jie Wang,Rudong Chen,Huiwen Zhang

doi:10.1186/1687-1812-2014-35

Jie Wang, Rudong Chen + Show 1 more

Open Access

https://doi.org/10.1186/1687-1812-2014-35

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Abstract

A new convex feasibility problem, the split equality problem (SEP), has been proposed by Moudafi and Byrne. The SEP was solved through the ACQA and ARCQA algorithms. In this paper the SEPs are extended to infinite-dimensional SEPs in Hilbert spaces and we established the strong convergence of a proposed algorithm to a solution of general split equality problems (GSEPs).

Highlights

1 Introduction In the present paper, we are concerned with the general split equality problem (GSEP) which is formulated as finding points x and y with the property:
To solve the SEP, Byrne and Moudafi put forward the alternating CQ-algorithm (ACQA) and the relaxed alternating CQ-algorithm (RACQA)
This paper aims at a study of an iterative algorithm improved by Eslamian [ ] for the GSEP in the Hilbert space

Summary

Introduction

We are concerned with the general split equality problem (GSEP) which is formulated as finding points x and y with the property:. Where Ci and Qj are two nonempty closed convex subsets of real Hilbert spaces H and H , respectively, H is a Hilbert space, A : H → H , B : H → H are two bounded linear operators. It generalizes the split equality problem (SEP), which is to find x ∈ C, y ∈ Q such that Ax = By [ ], as well as the split feasibility problem (SFP). {τ (n)}n≥n is a nondecreasing sequence verifying limn→∞ τ (n) = ∞, and for all n ≥ n , the following two estimates hold: tτ (n) ≤ tτ (n)+ , tn ≤ tτ (n)+

Si with

Note that for each

All conditions of