$b$-metric spaces with a graph and best proximity points for some contractions
محورهای موضوعی : Fixed point theory
1 - Department of Mathematics, Payame Noor University, Tehran, Iran
2 - Department of Mathematics, Payame Noor University, Tehran, Iran
کلید واژه: fixed point, Best proximity point, $G$-continuous mapping,
چکیده مقاله :
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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