Relation-theoretic coincidence and common fixed point results under (F,R)g $(F,\mathcal{R})_{g}$-contractions with an application

Abstract

Abstract In this paper, we begin with some observations on F-contractions. Thereafter, we introduce the notion of (F,R)g $(F,\mathcal{R})_{g}$-contractions and utilize the same to prove some coincidence and common fixed point results in the setting of metric spaces endowed with binary relations. An example is also given to exhibit the utility of our results. We also deduce some consequences in the setting of ordered metric spaces. As an application, we investigate the existence and uniqueness of a solution of integral equation of Volterra type.

Keywords

• Fixed point
• F-contraction
• Coincidence point
• Common fixed point
• Binary relation
• Integral equation