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Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces. (English) Zbl 1114.49008
Summary: 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 [J. Optimization Theory Appl. 121, No. 1, 203–210 (2004; Zbl 1056.49017); Adv. Nonlinear Var. Inequal. 7, No. 2, 155–164 (2004; Zbl 1079.49011); Appl. Math. Lett. 18, No. 11, 1286–1292 (2005; Zbl 1099.47054)], N. H. Xiu and J. Z. Zhang [J. Optimization Theory Appl. 115, No. 1, 211–230 (2002; Zbl 1091.49011)] and H. Nie, Z. Liu, K. H. Kim and S. M. Kang [Adv. Nonlinear Var. Inequal. 6, No. 2, 91–99 (2003; Zbl 1098.47055)].

MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators