Structure for $g$-Metric Spaces and Related Fixed Point Theorems
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| Format: | Preprint |
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2018
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| _version_ | 1866916474245873664 |
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| author | Choi, Hayoung Kim, Sejong Yang, Seung Yeop |
| author_facet | Choi, Hayoung Kim, Sejong Yang, Seung Yeop |
| contents | In this paper, we propose a generalized notion of a distance function, called a $g$-metric. The $g$-metric with degree $n$ is a distance of $n+1$ points, generalizing the ordinary distance between two points and $G$-metric between three points. Indeed, it is shown that the $g$-metric with degree 1 (resp. degree 2) is equivalent to the ordinary metric (resp. the $G$-metric). Fundamental properties and several examples for the $g$-metric are also given. Moreover, topological properties on the $g$-metric space including the convergence of sequences and the continuity of mappings on the $g$-metric space are studied. Finally, we generalize some well-known fixed point theorems including Banach contraction mapping principle and Ćirić fixed point theorem in the $g$-metric space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1804_03651 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Structure for $g$-Metric Spaces and Related Fixed Point Theorems Choi, Hayoung Kim, Sejong Yang, Seung Yeop General Topology 47H10, 54H25, 37C25, 54E99 In this paper, we propose a generalized notion of a distance function, called a $g$-metric. The $g$-metric with degree $n$ is a distance of $n+1$ points, generalizing the ordinary distance between two points and $G$-metric between three points. Indeed, it is shown that the $g$-metric with degree 1 (resp. degree 2) is equivalent to the ordinary metric (resp. the $G$-metric). Fundamental properties and several examples for the $g$-metric are also given. Moreover, topological properties on the $g$-metric space including the convergence of sequences and the continuity of mappings on the $g$-metric space are studied. Finally, we generalize some well-known fixed point theorems including Banach contraction mapping principle and Ćirić fixed point theorem in the $g$-metric space. |
| title | Structure for $g$-Metric Spaces and Related Fixed Point Theorems |
| topic | General Topology 47H10, 54H25, 37C25, 54E99 |
| url | https://arxiv.org/abs/1804.03651 |