Fixed point results for various contractions in parametric and fuzzy b-metric spaces

Volume 8, Issue 5, pp 719--739 http://dx.doi.org/10.22436/jnsa.008.05.24

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Authors

Nawab Hussain - Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589,, Saudi Arabia. Peyman Salimi - Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, Rasht, Iran. Vahid Parvaneh - Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran.

Abstract

The notion of parametric metric spaces being a natural generalization of metric spaces was recently introduced and studied by Hussain et al. [A new approach to fixed point results in triangular intuitionistic fuzzy metric spaces, Abstract and Applied Analysis, Vol. 2014, Article ID 69-139, 16 pp]. In this paper we introduce the concept of parametric b-metric space and investigate the existence of fixed points under various contractive conditions in such spaces. As applications, we derive some new fixed point results in triangular partially ordered fuzzy b-metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results.

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Keywords

• Fixed point theorem
• fuzzy b-metric spaces
• contractions.

MSC

•  54H25
•  54A40
•  54E50

References

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