Elsevier

Applied Mathematics Letters

Volume 19, Issue 12, December 2006, Pages 1320-1326
Applied Mathematics Letters

An existence result for generalized vector equilibrium problems without pseudomonotonicity

https://doi.org/10.1016/j.aml.2005.09.010Get rights and content
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Abstract

In this work, we introduce and study a class of generalized vector equilibrium problems for multifunctions which includes a number of generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. By using the KKM–Fan theorem and Nadler’s result, we prove an existence theorem for solutions for this class of generalized vector equilibrium problems in Banach spaces. Applications to generalized vector variational-like inequalities are given.

Keywords

Generalized vector equilibrium problem
Generalized vector variational-like inequalities
KKM-map
Hausdorff metric

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