Algorithms of common solutions to quasi variational inclusion and fixed point problems

Shi Sheng Zhang, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

110 Citations (Scopus)

Abstract

The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich (Ekonomika i Matematicheskie Metody, 1976, 12(4):747-756), but also extend and replenish the corresponding results obtained by Iiduka and Takahashi (Nonlinear Anal TMA, 2005, 61(3):341-350), Takahashi and Toyoda (J Optim Theory Appl, 2003, 118(2):417-428), Nadezhkina and Takahashi (J Optim Theory Appl, 2006, 128(1):191-201), and Zeng and Yao (Taiwanese Journal of Mathematics, 2006, 10(5):1293-1303).
Original languageEnglish
Pages (from-to)571-581
Number of pages11
JournalApplied Mathematics and Mechanics (English Edition)
Volume29
Issue number5
DOIs
Publication statusPublished - 1 May 2008

Keywords

  • Fixed point
  • Inversestrongly monotone mapping
  • Metric projection
  • Multi-valued maximal monotone mapping
  • Nonexpansive mapping
  • Variational inclusion

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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