Coupled fixed point results for new classes of functions on ordered vector metric space

Çevik C., Özeken Ç. C.

ACTA MATHEMATICA HUNGARICA, vol.172, no.1, pp.1-18, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 172 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1007/s10474-024-01393-3
  • Journal Name: ACTA MATHEMATICA HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet
  • Page Numbers: pp.1-18
  • Keywords: 46A19, 46A40, 47B60, 47H10, 54H25, coupled fixed point, fixed point, partial ordered metric space, Riesz space, vector metric space
  • Gazi University Affiliated: Yes

Abstract

The contraction condition in the Banach contraction principle forces a function to be continuous. Many authors overcome this obligation and weaken the hypotheses via metric spaces endowed with a partial order. In this paper, we present some coupled fixed point theorems for the functions having mixed monotone properties on ordered vector metric spaces, which are more general spaces than partially ordered metric spaces. We also define the double monotone property and investigate the previous results with this property. In the last section, we prove the uniqueness of a coupled fixed point for non-monotone functions. In addition, we present some illustrative examples to emphasize that our results are more general than the ones in the literature.