Fixed Points,Continuous Selections,and Existence of Solution of Optimization-Related Problems |
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Authors: | Phan Quoc Khanh |
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Affiliation: | Department of Mathematics, International University, Vietnam National University Hochiminh City, Hochiminh City, Vietnam |
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Abstract: | We propose a definition of a generalized type of Knaster–Kuratowski–Mazurkiewicz (KKM) mappings, called a weak T-KKM mapping, and a corresponding weak KKM property. A new extension of the Fan–Glicksberg fixed-point theorem is established. Sufficient conditions for the existence of a continuous selection, a fixed point of a composition, and a coincidence point are also provided. Then, we use the obtained results to study the existence of solutions to various optimization-related problems. Discussions and detailed examples are included as well to compare our results with existing ones and to explain their advantages in many situations. |
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Keywords: | Coincidence points continuous selections equilibria existence of solutions fixed points GFC-spaces quasivariational inclusions variational relations |
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