Abstract:
In this paper, we introduce an extended rectangular fuzzy b-metric space which generalizes rectangular fuzzy b-metric space and rectangular fuzzy metric space. We show that an extended rectangular fuzzy b-metric space is not Hausdorff. A Banach fixed point theorem is proved as a special case of our main result where a Ćirić type contraction was employed. Our main result generalizes some comparable results in rectangular fuzzy b-metric space and rectangular fuzzy metric space. We provide some examples to support the concepts and results presented herein. As an application of our result, we obtain the existence of the solution of the integral equation.