Property P in modular metric spaces

Abstract

Introduction/purpose: The aim of this paper is to present the concept of the generalized ∅−weak contractive condition involving various combinations of d(x,y) in modular metric spaces. Methods: Conventional theoretical methods of functional analysis. Results: This study presents the result of (Murthy & Vara Prasad, 2013) for a single-valued mapping satisfying a generalized ∅ −weak contractive condition involving various combinations of d(x,y). It is generalized in the setting of modular metric spaces, and then it is proved that this singlevalued map satisfies the property P. In the end, an example is given in support of the result. Conclusion: With proper generalisations, it is possible to formulate wellknown results of classical metric spaces to the case of modular metric spaces.

Keywords

• fixed point
• ∅ −weak contraction
• modular metric spaces
• property p