NEW TOPOLOGY ON M-METRIC SPACE

Subject Areas : Analyze

مهدی اسدی ¹ , Farshid Khojasteh ²

1 - Department of Mathematics, Zanjan Branch, Islamic Azad Yniversity, Zanjan, Iran
2 - Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran.

Received: 2022-01-15 Accepted : 2022-12-05 Published : 2024-01-18

Keywords: m -متر, فضای M -متری, متر جزئی,

Abstract :

Main Part: In this article, we provide a new definition of M-metric space. By presenting the topology of this space, while examining some of its properties, we show that the limit of a sequence is not necessarily unique. In the following, by defining a new topology, we state that it is weaker than the previously defined topology. ----------------------------------------------------------- Detail: In1994 in [1] Matthews introduced the notion of a partial metric space and proved the contraction principle of Banach in this new framework. Next, many fixed-point theorems in partial metric spaces have been given by several mathematicians. In this paper, we extend the p-metric space to an M-metric space, and we shall show that our definition is a real generalization of the p-metric by presenting some examples. Keywords: M-metric space; Pritial metric space. Mathematics Subject Classification [2010]: 54H25, 47H10. References [1] S. Matthews, Partial metric topology. Ann. N.Y. Acad. Sci. 728, 183-197 (1994) [2] Mehdi Asadi, Erdal Karapınar and Peyman Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces, Journal of Inequalities and Applications 2014, 2014:18

References:


[1] S. Matthews, Partial metric topology. Ann. N.Y. Acad. Sci. 728, 183-197 (1994)

[2] Mehdi Asadi, Erdal Karapınar and Peyman Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces, Journal of Inequalities and Applications 2014, 2014:18

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