New fixed point results in quasi-metric spaces and applications in fractals theory

Abstract

Abstract In this paper, we prove some fixed point theorems for ψF-contractions in the framework of quasi-metric spaces generalizing and improving several similar results in metric spaces. At the same time, we consider iterated function systems consisting of ψF-contractions on quasi-metric spaces, and we give some sufficient conditions for the existence and uniqueness of their attractor which is, generally, a fractal. Some illustrative examples are provided.

Keywords

• Quasi-metric space
• Forward (backward) F-contraction
• Picard operator
• Iterated function system
• Fractals