Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces

S. S. Chang, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

78 Citations (Scopus)

Abstract

The approximate solvability of a generalized system for relaxed cocoercive nonlinear variational inequality in Hilbert spaces is studied, based on the convergence of projection methods. The results presented in this paper extend and improve the main results of [R.U. Verma, Generalized system for relaxed cocoercive variational inequalities and its projection methods, J. Optim. Theory Appl. 121 (1) (2004) 203-210; R.U. Verma, Generalized class of partial relaxed monotonicity and its connections, Adv. Nonlinear Var. Inequal. 7 (2) (2004) 155-164; R.U. Verma, General convergence analysis for two-step projection methods and applications to variational problems, Appl. Math. Lett. 18 (11) (2005) 1286-1292; N.H. Xiu, J.Z. Zhang, Local convergence analysis of projection type algorithms: Unified approach, J. Optim. Theory Appl. 115 (2002) 211-230; H. Nie, Z. Liu, K.H. Kim, S.M. Kang, A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings, Adv. Nonlinear Var. Inequal. 6 (2) (2003) 91-99].
Original languageEnglish
Pages (from-to)329-334
Number of pages6
JournalApplied Mathematics Letters
Volume20
Issue number3
DOIs
Publication statusPublished - 1 Mar 2007

Keywords

  • Cocoercive mapping
  • Convergence of projection method
  • Projection method
  • Relaxed cocoercive mapping
  • Relaxed cocoercive nonlinear variational inequality

ASJC Scopus subject areas

  • Applied Mathematics

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