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Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices

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Open access
Authors
Kong, D.
Liu, L.
Wu, Yong Hong
Date
2014
Type
Journal Article

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Kong, D. and Liu, L. and Wu, Y.H. 2014. Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices. Fixed Point Theory and Applications. 2014 (18): pp. 1-10.
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Fixed Point Theory and Applications
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This article is published under the Open Access publishing model and distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/2.0/ Please refer to the licence to obtain terms for any further reuse or distribution of this work.

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Abstract

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.