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doi:10.1016/j.aml.2006.04.017 
Copyright © 2006 Elsevier Ltd All rights reserved.
Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces
Received 5 July 2005;
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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].
Keywords: Relaxed cocoercive nonlinear variational inequality; Projection method; Relaxed cocoercive mapping; Cocoercive mapping; Convergence of projection method
