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A new approach to generalize metric functions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 24، دوره 14، شماره 3، خرداد 2023، صفحه 279-298 اصل مقاله (1.87 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27489.3619 | ||
| نویسندگان | ||
| Abhishikta Das1؛ Anirban Kundu1؛ Tarapada Bag* 2 | ||
| 1Department of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan-731235, Birbhum, West Bengal, India | ||
| 2Department of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan-731235, Birbhum, West Bengal, India | ||
| تاریخ دریافت: 24 خرداد 1401، تاریخ بازنگری: 11 شهریور 1401، تاریخ پذیرش: 27 شهریور 1401 | ||
| چکیده | ||
| This article consists of a new concept of generalized metric space, called $\phi$-metric space which is developed by making a suitable modification in the `triangle inequality. The notion of $\phi$-metric generalizes the concept of some existing metrizable generalized spaces like S-metric, b-metric, etc. It is shown that one can easily construct a $\phi$-metric from those generalized metric functions and the notion of convergence of a sequence on those generalized metric spaces are identical with the respective induced $\phi$-metric spaces. Moreover, $\phi$-metric space is metrizable and its properties are pretty similar to the metric functions. So $\phi$-metric functions substantially may play the role of metric functions. Also, the structure of $\phi$-metric space is studied and some well-known fixed point theorems are established. | ||
| کلیدواژه‌ها | ||
| φ-metric؛ φ-metric spaces؛ generalized distance function؛ metrizability | ||
| مراجع | ||
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