Further on set-valued equilibrium problems in the pseudo-monotone case and applications to Browder variational inclusions |
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Authors: | Boualem Alleche Vicen?iu D R?dulescu |
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Institution: | 1.Laboratoire LPTEA, Faculté des Sciences,Université de Médéa,Médéa,Algeria;2.Faculty of Applied Mathematics,AGH University of Science and Technology,Kraków,Poland;3.Institute of Mathematics “Simion Stoilow” of the Romanian Academy,Bucharest,Romania |
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Abstract: | This paper deals with set-valued equilibrium problems under conditions of pseudo-monotonicity. Concepts such as strict quasi-convexity, hemicontinuity and pseudo-monotonicity for extended real set-valued mappings are introduced and applied to obtain results on the existence of solutions of set-valued equilibrium problems generalizing those in the literature in the pseudo-monotone case. Applications to Browder variational inclusions under weakened conditions are given. In particular, it is shown that the upper semicontinuity from line segments of the involved pseudo-monotone set-valued operator is not needed in the whole space when solving Browder variational inclusions. |
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