Variational-Like Inequalities and Equilibrium Problems with Generalized Monotonicity in Banach Spaces

N. K. Mahato and C. Nahak

Advances in Operations Research, 2012, vol. 2012, 1-15

Abstract:

We introduce the notion of relaxed (Ï -θ)-η-invariant pseudomonotone mappings, which is weaker than invariant pseudomonotone maps. Using the KKM technique, we establish the existence of solutions for variational-like inequality problems with relaxed (Ï -θ)-η-invariant pseudomonotone mappings in reflexive Banach spaces. We also introduce the concept of (Ï -θ)-pseudomonotonicity for bifunctions, and we consider some examples to show that (Ï -θ)-pseudomonotonicity generalizes both monotonicity and strong pseudomonotonicity. The existence of solution for equilibrium problem with (Ï -θ)-pseudomonotone mappings in reflexive Banach spaces are demonstrated by using the KKM technique.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaor:648070

DOI: 10.1155/2012/648070

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