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Erschienen in:
01.10.2012 | Applied mathematics
Weakly relaxed α-pseudomonotonicity and equilibrium problem in Banach spaces
Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2012
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Abstract
In this paper, we introduce the weakly relaxed α-pseudomonotone mapping which generalizes the class of pseudomonotone mappings. Some examples are given which show that the weakly relaxed α-pseudomonotonicity is a proper generalization of pseudomonotonicity for both scalar and vector valued bi-functions. Using the KKM technique, we establish the existence of solutions of equilibrium problems and vector equilibrium problems with weakly relaxed α-pseudomonotonicity in the reflexive Banach spaces. The present work extends some corresponding results of the variational-like inequalities (Fang and Huang in J. Optim. Theory Appl. 118:327–338, 2003; Lee and Lee in J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 11: 231–242, 2004) to equilibrium problems.