The Generalized Iterated Function System and Common Attractors of Generalized Hutchinson Operators in Dislocated Metric Spaces

Abstract

In this paper, we present the generalized iterated function system for the construction of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors’ problems of rational contraction maps in the framework of dislocated metric spaces is also established. Moreover, the generalized collage theorem is also obtained in dislocated metric spaces.

Keywords

• Hutchinson operator
• generalized iterated function system
• fractal
• generalized rational contraction
• set-valued mapping
• common fixed point