Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices
In this paper, we extend and prove Ky Fan’s Theorem for discontinuous increasing maps f in a Banach lattice X when f has no compact conditions. The main tools of analysis are the variational characterization of the generalized projection operator and order-theoretic fixed-point theory. Moreover, we...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
SpringerOpen
2014
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/26654 |
| Summary: | In this paper, we extend and prove Ky Fan’s Theorem for discontinuous increasing maps f in a Banach lattice X when f has no compact conditions. The main tools of analysis are the variational characterization of the generalized projection operator and order-theoretic fixed-point theory. Moreover, we establish a sequence {xn} which converges strongly to the unique best approximation point. As an application of our best approximation theorems, a fixed-point theorem for non-self maps is established and proved under some conditions. Our results generalize and improve many recent results obtained by many authors. |
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