Fixed point theorem and iterated function system in φ-metric modular space

Abstract

Abstract We introduce and study the concept of φ-metric modular space and, then define φ-α-Meir-Keeler contraction on it and explore its fixed point. Further, we define the Hausdorff distance between two non-empty compact subsets of the considered space. Some topological properties of φ-metric modular space are also explored. Additionally, we prove the existence of the attractor (fractal) of the IFS consisting of φ-α-Meir-Keeler contractions.

Keywords

• Metric modular space
• φ-metric modular space
• φ-α-Meir-Keeler contraction
• Fixed point
• Iterated function system
• Attractor