A fixed point theorem for F-PGA: Contractions on complete metric spaces

Abstract

Piri et al. had (H. Piri, S. Rahrovi, P. Kumam, Generalization of Khan fixed point theorem, J. Math. Computer Sci., 17 (2017), 76–83.) established generalized Khan contraction in 2017. By considering the concept of F-contraction on generalized Khan contraction, the authors have initiated the idea of F-Khan contraction and established the existence and uniqueness of fixed point. In the present paper, the authors have introduced the following more general versions of contraction map: . The extension of generalized Khan- contraction viz. PGA-contraction has been initiated at the first step. . In the next step, referring the concept of F- contraction, the more general form of PGA- contraction, in particular F-PGA-contraction has been defined. The existence and uniqueness of a fixed point has been established in view of F-PGA contraction.