Rendiconti del Circolo Matematico di Palermo

, Volume 61, Issue 3, pp 361–383 | Cite as

Common coupled fixed point theorems for \(w^*\)-compatible mappings without mixed monotone property

  • Wutiphol Sintunavarat
  • Adrian Petruşel
  • Poom Kumam
Article

Abstract

In this paper, we show that the mixed \(g\)-monotone property in coupled coincidence point theorems can be replaced by generalized property. Hence, these results can be applied in a much wider class of problems. We also study the condition for the uniqueness of a common coupled fixed point and give some example of nonlinear contraction mappings where the existence of the common coupled fixed point cannot be obtained by the mixed monotone property, but it follows by our results. At the end of this paper, we give an open problems for further investigation.

Keywords

Cone metric space Coupled common fixed point Coupled coincidence point \(w^*\)-compatible maps Mixed \(g\)-monotone property (F, g)-invariant set 

Mathematics Subject Classification (2010)

47H10 54H25 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Wutiphol Sintunavarat
    • 1
  • Adrian Petruşel
    • 2
  • Poom Kumam
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceKing Mongkut’s University of Technology Thonburi (KMUTT)BangkokThailand
  2. 2.Department of MathematicsBabeş-Bolyai University Cluj-NapocaCluj-NapocaRomania

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