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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 in a real partially ordered reflexive, strictly convex, and smooth Banach space . 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, Hindawi, vol. 2015, pages 1-7, July.
    • Handle: RePEc:hin:jnlaaa:165053
    DOI: 10.1155/2015/165053
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