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Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

Chowdhury, Mohammad — 1998

Serdica Mathematical Journal

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar. Existence theorems of generalized variational inequalities and generalized complementarity problems are obtained in topological vector spaces for demi operators which are upper hemicontinuous along line segments in a convex set X. Fixed point theorems are also given in Hilbert spaces for set-valued operators T which are upper hemicontinuous along line segments...

Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

Mohammad Chowdhury;  Kok-Keong Tan — 2010

Open Mathematics

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s...

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