On Banach contraction principles in fuzzy metric spaces


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	On Banach contraction principles in fuzzy metric spaces


	Fixed Point Theory, Volume 19, No. 1, 2018, 235-248, February 1st, 2018 DOI: 10.24193/fpt-ro.2018.1.19 Authors: Valentín Gregori, Juan-José Miñana and Almanzor Sapena Abstract: In this paper we discuss the concept of Cauchy sequence due to Grabiec, that we call G-Cauchy, in the context of fuzzy metric spaces. It leads to introduce and study a concept of weak $-completeness in fuzzy and classical context. Then, we generalize the celebrated Grabiec's fuzzy Banach Contraction Principle. Also, we extend the Mihet's fixed point theorem given for weak B-contractive mappings. Key Words and Phrases: Fixed point theorem, fuzzy metric space, G-Cauchy sequence. 2010 Mathematics Subject Classification: 54A40, 54D35, 54E50. Published on-line: February 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents