The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces
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 t...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Science in China Press
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/42595 |
| Summary: | 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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