An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem. (13th March 2014)

• Record Type: Journal Article
• Authors: Shi, Luoyi; Chen, Ru Dong; Wu, Yu Jing
• Other Names: Song Yisheng Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-03-13
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/620813
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : The multiple-sets split equality problem (MSSEP) requires finding a point x ∈ ∩ i = 1 N C i, y ∈ ∩ j = 1 M Q j such that A x = B y, where N and M are positive integers, { C 1, C 2, …, C N } and { Q 1, Q 2, …, Q M } are closed convex subsets of Hilbert spaces H 1, H 2, respectively, and A : H 1 → H 3, B : H 2 → 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.