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 single-valued 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 well-known results of classical metric spaces to the case of modular metric spaces.