Research article

µ-extended fuzzy b-metric spaces and related fixed point results

  • Received: 01 February 2020 Accepted: 01 June 2020 Published: 15 June 2020
  • MSC : 47H10, 54H25

  • 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.

    Citation: Badshah-e-Rome, Muhammad Sarwar, Thabet Abdeljawad. µ-extended fuzzy b-metric spaces and related fixed point results[J]. AIMS Mathematics, 2020, 5(5): 5184-5192. doi: 10.3934/math.2020333

    Related Papers:

  • 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.


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