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Zbl 1114.49008
Chang, S.S.; Joseph Lee, H.W.; Chan, C.K.
Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces. (English)
[J] Appl. Math. Lett. 20, No. 3, 329-334 (2007). ISSN 0893-9659

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 {\it 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)], {\it N. H. Xiu} and {\it J. Z. Zhang} [J. Optimization Theory Appl. 115, No. 1, 211--230 (2002; Zbl 1091.49011)] and {\it H. Nie, Z. Liu, K. H. Kim} and {\it S. M. Kang} [Adv. Nonlinear Var. Inequal. 6, No. 2, 91--99 (2003; Zbl 1098.47055)].

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators

Keywords: relaxed cocoercive nonlinear variational inequality; projection method; relaxed cocoercive mapping; cocoercive mapping; convergence of projection method

Citations: Zbl 1056.49017; Zbl 1079.49011; Zbl 1099.47054; Zbl 1091.49011; Zbl 1098.47055

Cited in: Zbl 1192.49016 Zbl 1189.49008 Zbl 1160.47051 Zbl 1153.49009 Zbl 1129.49020

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