J. Korean Math. Soc. 2003; 40(2): 195-205
Printed March 1, 2003
Copyright © The Korean Mathematical Society.
Y. J. Cho, Y. P. Fang, N. J. Huang, and K. H. Kim
Gyeongsang National University, Sichuan University, Sichuan University, Gyeongsang National University
In this paper, we introduce and study a new class of generalized strongly nonlinear variational inequalities with set-valued mappings. By using the KKM technique, we prove the existence and uniqueness of solution for this class of generalized set-valued strongly nonlinear variational inequalities in reflexive Banach spaces. Our results include the main results of Verma [16], [17] as special cases.
Keywords: strongly nonlinear variational inequality, set-valued mapping, generalized monotone type mapping, generalized Lipschitzian type mapping, the KKM mapping
MSC numbers: 47H06, 49J30, 49J40
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