The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces
Keyword(s):
We prove that Fan’s theorem is true for discontinuous increasing mappingsfin a real partially ordered reflexive, strictly convex, and smooth Banach spaceX. The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point theory. Moreover, we get some properties of the generalized projection operator in Banach spaces. As applications of our best approximation theorems, the fixed point theorems for non-self-maps are established and proved under some conditions. Our results are generalizations and improvements of the recent results obtained by many authors.
2003 ◽
Vol 2003
(1)
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pp. 33-47
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2005 ◽
Vol 2005
(5)
◽
pp. 789-801
Keyword(s):
2019 ◽
Vol 8
(10S)
◽
pp. 85-89
2010 ◽
Vol 258
(10)
◽
pp. 3452-3468
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