A fixed point result of weakly contractive operators in generalized metric spaces

Abstract

In this note, by using basic properties of the recently introduced concepts of generalized metric spaces, new conditions for the existence of a fixed point for weakly type contractive operator which sends a closed subset into the ambient space under consideration are examined. Our obtained result extends and unifies its corresponding ideas in metric and modular spaces. A comparative non-trivial example is provided to show the novelty and preeminence of our proposed notion.

Keywords

• fixed point
• generalized metric space
• modular space
• weakly contractive