Abstract
The aim of this paper is to introduce fuzzy generalised weak contractive condition for a pair of self maps in a fuzzy metric space,which is in accordance with the theory of metric spaces given by Rhoades (Nonlinear Analysis 47:2683–2693, 2001). Our results generalize existing fuzzy contraction (by Gregori and Sapena (Fuzzy Sets System 125:245–252, 2002), which is for only one self map. Using this, we establish a unique common fixed point theorem for two self-maps through weak compatibility. The article includes an example, in support of our results. Also an application we established, for the existence and uniqueness of a solution of Fredholm non-linear integral equation in the setting of fuzzy metric space.
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