The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces
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Authors
Liu, Lishan
Kong, D.
Wu, Yong Hong
Date
2015Type
Journal Article
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Liu, L. and Kong, D. and Wu, Y.H. 2015. The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces. Science China Mathematics. 58 (12): pp. 2581-2592.
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Science China Mathematics
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Faculty
Faculty of Science and Engineering
School
Department of Mathematics and Statistics
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Abstract
We discuss Ky Fan’s theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors.
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