Weakly relaxed ?-pseudomonotonicity and equilibrium problem in Banach spaces
In this paper, we introduce the weakly relaxed ?-pseudomonotone mapping which generalizes the class of pseudomonotone mappings. Some examples are given which show that the weakly relaxed ?-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 ?-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. 118:327338, 2003; Lee and Lee in J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 11: 231242, 2004) to equilibrium problems.
weakly relaxed ?-pseudomonotonicity equilibrium problems vector equilibrium problems kkm mappings 91b52 90c30