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

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  • N. K. Mahato
  • C. Nahak

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.

Suggested Citation

  • N. K. Mahato & C. Nahak, 2012. "Variational-Like Inequalities and Equilibrium Problems with Generalized Monotonicity in Banach Spaces," Advances in Operations Research, Hindawi, vol. 2012, pages 1-15, January.
    • Handle: RePEc:hin:jnlaor:648070
    DOI: 10.1155/2012/648070
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