Abstract and Applied Analysis

The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces

Dezhou Kong, Lishan Liu, and Yonghong Wu

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Abstract

We prove that Fan’s theorem is true for discontinuous increasing mappings f in a real partially ordered reflexive, strictly convex, and smooth Banach space X . 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.

Article information

Source
Abstr. Appl. Anal., Volume 2015, Special Issue (2015), Article ID 165053, 7 pages.

Dates
First available in Project Euclid: 17 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1439816292

Digital Object Identifier
doi:10.1155/2015/165053

Mathematical Reviews number (MathSciNet)
MR3378555

Zentralblatt MATH identifier
06929069

Citation

Kong, Dezhou; Liu, Lishan; Wu, Yonghong. The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces. Abstr. Appl. Anal. 2015, Special Issue (2015), Article ID 165053, 7 pages. doi:10.1155/2015/165053. https://projecteuclid.org/euclid.aaa/1439816292


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