New Fuzzy Fixed Point Results in Generalized Fuzzy Metric Spaces With Application to Integral Equations

Abstract

In this paper, we introduce the notion of generalized fuzzy metric space. Many topological spaces like fuzzy metric spaces, fuzzy $b$ -metric spaces and dislocated fuzzy metric spaces have been generalized by this new generalized fuzzy metric space. We prove the Banach contraction principle and Ćirić’s quasi-contraction theorem in the setting of generalized fuzzy metric space and furnish an example to illustrate our results. As consequences of our results we obtain Jleli and Samet and many other authors recent results as corollaries. An application related to our main result for nonlinear integral equation is also presented.

Keywords

• Fuzzy metric space
• b-metric space%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> fuzzy <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">b</italic>-metric space
• generalized metric space