On new type of \(F\)-contractive mapping for quasipartial \(b\)-metric spaces and some results of fixed-point theorem and application (Q2228195)

Summary: In this paper, we introduce the concept of new type of \(F\)-contractive type for quasipartial \(b\)-metric spaces and some definitions and lemmas. Also, we will prove a new fixed-point theorem in quasipartial \(b\)-metric spaces for \(F\)-contractive type mappings. In addition, we give an application which illustrates a situation when Banach's fixed-point theorem for complete quasipartial \(b\)-metric spaces cannot be applied, while the conditions of our theorem are satisfying.