<em>µ</em>-extended fuzzy <em>b</em>-metric spaces and related fixed point results

Abstract

This paper introduces the notion of $\mu$-extended fuzzy $b$-metric space for extending the concept of fuzzy $b$-metric space and obtains an analogue of Banach fixed point result. Using functions $\alpha(x,y)$ and $\mu(x,y)$, the corresponding triangle inequality in $\mu$-extended fuzzy $b$-metric space is given as follows $$M( \upsilon,\omega,\alpha(\upsilon,\omega)s+\mu(\upsilon,\omega)t)\geq M(\upsilon,\nu,s)*M(\nu,\omega,t)\ \ \forall \upsilon,\nu,\omega \in X. $$ An analogue of Banach fixed point result is established. Besides, an example is given to confirm validity of this theorem.

Keywords

• fuzzy metric space
• extended fuzzy b-metric space
• µ-extended fuzzy b-metric space
• fixed point