Banach Contraction Theorem on Extended Fuzzy Cone b-metric Space

Vishal Gupta, Surjeet Singh Chauhan, Ishpreet Kaur Sandhu

Abstract

In this paper, a generalization of b-metric space is introduced named as extended fuzzy cone b-metric space. A new contractive mapping, extended fuzzy cone b-contractive mapping is defined and a modified form of Banach Contraction Theorem is proved for single and pair of mappings which is termed as extended fuzzy cone b-Banach Contraction Theorem. The derived results are applied on Fredholm Integral Equations to obtain a unique solution.