Continuous Selections, Collectively Fixed Points and Weak Knaster–Kuratowski–Mazurkiewicz Mappings in Optimization

P. Q. Khanh (), V. S. T. Long () and N. H. Quan ()
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P. Q. Khanh: International University of Hochiminh City
V. S. T. Long: Cao Thang College of Technology
N. H. Quan: University of Science of Hochiminh City

Journal of Optimization Theory and Applications, 2011, vol. 151, issue 3, No 8, 552-572

Abstract: Abstract We prove theorems on continuous selections, collectively fixed points, collectively coincidence points, weak Knaster–Kuratowski–Mazurkiewicz mappings and provide their applications in various optimization-related problems. Each of our theorems is demonstrated by using its preceding assertions. The results contain and improve a number of existing ones in the recent literature. They are shown to be also more advantageous in applications in optimization.

Keywords: Continuous selections; Collectively fixed points and coincidence points; Weak Knaster–Kuratowski–Mazurkiewicz theorems; Variational relations; Bilevel optimization; Nash equilibria; Minimax inequalities (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-011-9889-0

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