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A topological characterization of the existence of fixed points and applications |
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| Authors: | Phan Quoc Khanh Nguyen Hong Quan |
| Institution: | 1. Department of Mathematics, International University of Hochiminh City, Hochiminh City, Vietnam;2. +84 988942043;3. Department of Mathematics and Computer Science, University of Science Hochiminh City, Hochiminh City, Vietnam |
| Abstract: | We prove a topological two‐way characterization of the existence of fixed‐points, without using linear or convexity structures and provide applications in optimization‐related problems. Such a characterization is also demonstrated for a fixed‐component point, a slight generalization of a fixed point. |
| Keywords: | Fixed‐points fixed‐component points coincidence points KKM‐structures KKM‐maps coercive conditions optimization‐related problems Nash equilibrium 54H25 91A06 91A10 49J53 |