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Zbl 1153.49009
Cho, Yeol Je; Qin, Xiaolong
Systems of generalized nonlinear variational inequalities and its projection methods. (English)
[J] Nonlinear Anal., Theory Methods Appl. 69, No. 12, A, 4443-4451 (2008). ISSN 0362-546X

Summary: Based on relaxed cocoercive monotonicity, a new generalized class of nonlinear variational inequality problems is presented. Our results improve and extend the recent ones announced by [{\it Z. Huang} and {\it A. Noor}, Appl. Math. Comput. 190, No. 1, 356--361 (2007; Zbl 1120.65080); {\it S. S. Chang, H. W. Joseph Lee} and {\it C. K. Chan}, Appl. Math. Lett. 20, No. 3, 329--334 (2007; Zbl 1114.49008); {\it R. U. Verma}, J. Optimization Theory Appl. 121, No. 1, 203--210 (2004; Zbl 1056.49017); {\it M. A. Noor}, Appl. Math. Lett. 1, No. 2, 119--122 (1988; Zbl 0655.49005)] and many others.

MSC 2000:: *49J40 Variational methods including variational inequalities
47H04 Set-valued operators
47H06 Accretive operators, etc. (nonlinear)
47J25 Methods for solving nonlinear operator equations (general)
65B05 Extrapolation to the limit
49M15 Methods of Newton-Raphson, Galerkin and Ritz types

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

Citations: Zbl 1120.65080; Zbl 1114.49008; Zbl 1056.49017; Zbl 0655.49005

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