Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results

Abstract

In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular $b$ -metric space, fuzzy $b$ -metric space, and extended fuzzy $b$ -metric space. We use $f,g,h,$ three noncomparable functions as follows: ${\mathfrak{m}}_q\left(\mu ,\eta ,t+s+w\right)\ge {\mathfrak{m}}_q\left(\mu ,\nu ,t/f\left(\mu ,\nu \right)\right)\ast {\mathfrak{m}}_q\left(\nu ,\xi ,s/g\left(\nu ,\xi \right)\right)\ast {\mathfrak{m}}_q\left(\xi ,\eta ,w/h\left(\xi ,\eta \right)\right)$ . We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. An example is presented to support our main results. We also apply our technique to the uniqueness for the solution of an integral equation.