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Zbl 1076.49004
Cai, Tao; Liu, Zeqing; Shim, Soo Hak; Kang, Shin Min
Approximation-solvability of a system of generalized nonlinear mixed variational inequalities. (English)
[J] Adv. Nonlinear Var. Inequal. 8, No. 1, 63-70 (2005). ISSN 1092-910X

Summary: We introduce and study a new class of systems of generalized nonlinear mixed variational inequalities and prove its equivalence with a class of fixed-point problems by making use of the properties of the subdifferential of a proper, convex and lower semi-continuous functional. We also construct a new iterative algorithm for solving this class of systems of inequalities and prove the existence and uniqueness of solutions and the convergence of iterative sequences generated by the algorithm.

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: generalized nonlinear mixed variational inequalities; strongly monotone mapping; algorithm; convergence; fixed-points

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Zentralblatt MATH Berlin [Germany]