Fuzzy double controlled metric spaces and related results

Abstract

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions alpha and beta in the triangular inequality as:

M-q (x, z, t alpha(x, y) + s beta(y, z)) >= M-q(x, y, t) * M-q (y, z, s).

We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.