## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 620813, 5 pages.

### An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem

Luoyi Shi, Ru Dong Chen, and Yu Jing Wu

#### Abstract

The multiple-sets split equality problem (MSSEP) requires finding a point $x\in {\cap}_{i=1}^{N}{C}_{i}$, $y\in {\cap}_{j=1}^{M}{Q}_{j}$ such that $Ax=By$, where $N$ and $M$ are positive integers, $\{{C}_{1},{C}_{2},\dots ,{C}_{N}\}$ and $\{{Q}_{1},{Q}_{2},\dots ,{Q}_{M}\}$ are closed convex subsets of Hilbert spaces ${H}_{1}$, ${H}_{2}$, respectively, and $A:{H}_{1}\to {H}_{3}$, $B:{H}_{2}\to {H}_{3}$ are two bounded linear operators. When $N=M=1$, the MSSEP is called the split equality problem (SEP). If $B=I$, then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. One of the purposes of this paper is to introduce an iterative algorithm to solve the SEP and MSSEP in the framework of infinite-dimensional Hilbert spaces under some more mild conditions for the iterative coefficient.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 620813, 5 pages.

**Dates**

First available in Project Euclid: 2 October 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1412278802

**Digital Object Identifier**

doi:10.1155/2014/620813

**Mathematical Reviews number (MathSciNet)**

MR3182296

**Zentralblatt MATH identifier**

1337.47103

#### Citation

Shi, Luoyi; Chen, Ru Dong; Wu, Yu Jing. An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 620813, 5 pages. doi:10.1155/2014/620813. https://projecteuclid.org/euclid.aaa/1412278802