Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities |
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Authors: | Lai-Jiu Lin Zenn-Tsuen Yu Li-Ping Lai |
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Institution: | a Department of Mathematics, National Changhua University of Education, Changhua 50058, Taiwan, ROC b Department of Electrical Engineering, Nan-Kai College, Nantour 542, Taiwan, ROC c Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India |
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Abstract: | In this paper, we establish some fixed point theorems for a family of multivalued maps under mild conditions. By using our fixed point theorems, we derive some maximal element theorems for a particular family of multivalued maps, namely the Φ-condensing multivalued maps. As applications of our results, we prove some general equilibrium existence theorems in the generalized abstract economies with preference correspondences. Further applications of our results are also given to minimax inequalities for a family of functions. |
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Keywords: | Fixed point theorems Maximal element theorems Φ-condensing multivalued maps Transfer compactly open valued maps Generalized abstract economies Minimax inequalities |
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