Coupled fixed point results for $alpha$-admissible Mizoguchi-Takahashi contractions in $b$-metric spaces with applications

Abstract

The aim of this paper is to establish some fixed point theorems for $alpha$-admissible Mizoguchi-Takahashi contractive mappings defined on a ${b}$-metric space which generalize the results of Gordji and Ramezani cite{Roshan6}. As a result, we obtain some coupled fixed point theorems which generalize the results of '{C}iri'{c} {et al.} cite{Ciric3}. We also present an application in order to illustrate the effectiveness of our results.

Keywords

• ${b}$-metric space
• Partially ordered set
• Coupled fixed point
• Mixed monotone property