Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2003; 40(2): 195-205

Printed March 1, 2003

Copyright © The Korean Mathematical Society.

Generalized set-valued strongly nonlinear variational inequalities in Banach spaces

Y. J. Cho, Y. P. Fang, N. J. Huang, and K. H. Kim

Gyeongsang National University, Sichuan University, Sichuan University, Gyeongsang National University

Abstract

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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