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Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets

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  • Jinlu Li
  • Ying Liu
  • Hongya Gao

Abstract

We apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure.

Suggested Citation

  • Jinlu Li & Ying Liu & Hongya Gao, 2014. "Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    • Handle: RePEc:hin:jnlaaa:580621
    DOI: 10.1155/2014/580621
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