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General system of \(A\)-monotone nonlinear variational inclusion problems with applications. (English) Zbl 1107.49012

Summary: Based on the notion of \(A\)-monotonicity, the solvability of a system of nonlinear variational inclusions using the resolvent operator technique is presented. The results obtained are new and general in nature.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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[1] VERMA, R. U., A-Monotonicity and Applications to Nonlinear Inchusion Problems, Journal of Applied Mathematics and Sotchastic Analysis, Vol. 17. No. 2, pp. 193–195, 2004. · Zbl 1064.49012 · doi:10.1155/S1048953304403013
[2] FANG, Y. P., and HUANG, N. J., H-Monotone Operator and Resolvent Operator Technique for Variational Inclusions, Applied Mathematics and Computation, Vol. 145, No. 2–3, pp. 795–803, 2003. · Zbl 1030.49008
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[5] VERMA, R. U., Nonlinear Variational and Constrained Hemivariational Inequalities Involving Relaxed Operators, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 77, No. 5, pp. 387–391, 1997. · Zbl 0886.49006 · doi:10.1002/zamm.19970770517
[6] HUANG, N. J., Generalized Nonlinear Implicit Quasivariational Inclusion and an Application to Implicit Variational Inequalities, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 79, No. 8, pp. 560–575, 1999.
[7] PANAGIOTOPOULOS, P. D., Hemivariational Inequalities and Their Applications in Mechanics and Engineering, Springer Verlag, New York, NY, 1993. · Zbl 0826.73002
[8] VERMA, R. U., Generalized System for Relaxed Cocoercive Variational Inequalities and Projection Methods, Jounral of Optimization Theory and Applications, Vol. 121, No. 1, 203–210, 2004. · Zbl 1056.49017
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