BPP and FP of cyclic $\mathcal{G}$-$(\varphi-\psi)$-weak contractive mappings in graphical metric spaces and their consequences

The main goal of this article is first to express a cyclic $\mathcal{G}$-$(\varphi-\psi)$-weak contractive mapping, and second to present the existence of their best proximity points and fixed points. Several consequences are as well prepared to show the efficiency of our main results. One of the most important issues of this work is that it can also involve all former papers introduced by taking comparable and $\varepsilon$-close members.