Gap functions and existence of solutions for generalized vector quasivariational inequalities

Long, Xian Jun; Huang, Nan Jing

doi:10.2140/involve.2008.1.183

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Gap functions and existence of solutions for generalized vector quasivariational inequalities

Xian Jun Long and Nan Jing Huang

Vol. 1 (2008), No. 2, 183–195

DOI: 10.2140/involve.2008.1.183

Abstract

The gap functions for generalized vector quasivariational inequalities in Hausdorff topological vector spaces are introduced, then using Fan–Knaster–Kuratowski–Mazurkiewicz (FKKM) theorem, some existence theorems for a class of generalized vector quasivariational inequalities under suitable assumptions are established. The obtained results extend and unify corresponding results in the literature.

Keywords

generalized vector quasivariational inequality, gap function, existence of solutions, FKKM theorem, set-valued mapping

Mathematical Subject Classification 2000

Primary: 49J40

Secondary: 47H04

Milestones

Received: 27 October 2007

Accepted: 27 October 2007

Published: 1 July 2008

Communicated by Ram U. Verma

Authors

Xian Jun Long
Department of Mathematics Sichuan University Chengdu, Sichuan 610064 China

Nan Jing Huang
Department of Mathematics Sichuan University Chengdu, Sichuan 610064 China

Vol. 1, No. 2, 2008