$b$-metric spaces with a graph and best proximity points for some contractions

الموضوعات :

K. Fallahi ¹ (Department of Mathematics, Payame Noor University, Tehran, Iran)
M. Ayobian ² (Department of Mathematics, Payame Noor University, Tehran, Iran)

تاريخ الإرسال : 22 الأربعاء , صفر, 1443 تاريخ التأكيد : 21 الجمعة , ربيع الثاني, 1443 تاريخ الإصدار : 26 الأربعاء , ربيع الثاني, 1443

الکلمات المفتاحية: fixed point, Best proximity point, $G$-continuous mapping,

ملخص المقالة :

In this paper, we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph. Then we support our main theorem by a non-trivial example and give some consequences of it for usual graphs.

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