On a system of generalized nonlinear variational inequalities
Commun. Korean Math. Soc. 2007 Vol. 22, No. 2, 247-258
Printed June 1, 2007
Jingchang Li, Zhenyu Guo, Zeqing Liu, Shin Min Kang
Dalian Vocational Technical College, Liaoning Normal University, Liaoning Normal University, Gyeongsang National University
Abstract : In this paper a new class of system of generalized nonlinear variational inequalities involving strongly monotone, relaxed cocoercive and relaxed generalized monotone mappings in Hilbert spaces is introduced and studied. Based on the projection method, an equivalence between the system of generalized nonlinear variational inequalities and the fixed point problem is established, which is used to suggest some new iterative algorithms for computing approximate solutions of the system of generalized nonlinear variational inequalities. A few sufficient conditions which ensure the existence and uniqueness of solution of the system of generalized nonlinear variational inequalities are given, and the convergence analysis of iterative sequences generated by the algorithms are also discussed.
Keywords : system of generalized nonlinear variational inequalities, iterative algorithms, solution, convergence
MSC numbers : 47J20, 49J40
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