On New Type of $F$-Contractive Mapping for Quasipartial $b$-Metric Spaces and Some Results of Fixed-Point Theorem and Application

Abstract

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.