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Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces

By SS Chang, HWJ Lee and CK Chan


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].Department of Applied Mathematic

Topics: Cocoercive mapping, Convergence of projection method, Projection method, Relaxed cocoercive mapping, Relaxed cocoercive nonlinear variational inequality
Publisher: Pergamon Press
Year: 2007
DOI identifier: 10.1016/j.aml.2006.04.017
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