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Systems of generalized nonlinear variational inequalities and its projection methods. (English) Zbl 1153.49009
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 [Z. Huang and A. Noor, Appl. Math. Comput. 190, No. 1, 356–361 (2007; Zbl 1120.65080); S. S. Chang, H. W. Joseph Lee and C. K. Chan, Appl. Math. Lett. 20, No. 3, 329–334 (2007; Zbl 1114.49008); R. U. Verma, J. Optimization Theory Appl. 121, No. 1, 203–210 (2004; Zbl 1056.49017); M. A. Noor, Appl. Math. Lett. 1, No. 2, 119–122 (1988; Zbl 0655.49005)] and many others.
MSC:
49J40Variational methods including variational inequalities
47H04Set-valued operators
47H06Accretive operators, dissipative operators, etc. (nonlinear)
47J25Iterative procedures (nonlinear operator equations)
65B05Extrapolation to the limit, deferred corrections
49M15Newton-type methods in calculus of variations