Best proximity point theorems by $K$, $C$ and $\mathcal{MT}$ types in $b$-metric spaces with an application

	Best proximity point theorems by $K$, $C$ and $\mathcal{MT}$ types in $b$-metric spaces with an application
International Journal of Nonlinear Analysis and Applications
دوره 12، شماره 2، بهمن 2021، صفحه 1317-1329 اصل مقاله (381.54 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.19156.2060
نویسندگان
Setareh Ghezellou¹؛ Mahdi Azhini²؛ Mehdi Asadi^* ³
¹Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
²Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
³Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran
چکیده
In this paper, we introduce the concept of weak $\mathcal{MT}-K$ rational cyclic and weak $\mathcal{MT}-C$ rational cyclic conditions and a combination of both conditions in what we call weak $\mathcal{MT}-KC$ rational cyclic condition. We investigate some best proximity points theorems for a pair of mappings that satisfy these conditions that have been established in $b$-metric spaces. Our results include an application to the nonlinear integral equation as well.
کلیدواژه‌ها
$b$-metric space؛ $mathcal{MT}$-function؛ Rational cyclic condition؛ Cyclic map؛ Best proximity point
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