Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

Abstract

The purpose of this paper is to define the notion of extended convex ℱ contraction by imposing less conditions on the function ℱ satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of b-metric spaces. In addition, some illustrative examples are provided to show the usability of the obtained results. Lastly, we use the obtained fixed-point results to find the fractals with respect to the iterated function systems in the framework of b-metric spaces. Furthermore, the variables involved in the b-metric space are symmetric, and symmetry plays an important role in solving the nonlinear problems defined in operator theory.

Keywords

• <i>b</i>-metric space
• fixed point
• Wardowski (or ℱ) contraction
• convex contraction
• fractals
• iterated function systems