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

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  • Dezhou Kong
  • Lishan Liu
  • Yonghong Wu

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.

Suggested Citation

  • Dezhou Kong & Lishan Liu & Yonghong Wu, 2015. "The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:165053
    DOI: 10.1155/2015/165053
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    References listed on IDEAS

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    1. D. Roux & S. P. Singh, 1989. "On some fixed point theorems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-4, January.
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