Best proximity results for proximal contractions in metric spaces endowed with a graph

Figures & data

Figure 1. $(x,x)\in \mathrm{\Delta }\forall x\in X$.

Figure 2. $(p,q)\in E_1$ where $p=(x1,y_1)$, $q=(u_1,v_1)\in S_1$ with $x_1\ge u_1$ and $y_1\ge v_1$.

Figure 3. $(s,t)\in E_2$ where $s=(x_2,y_2)$, $t=(u_2,v_2)\in S_2$ with $x_2\le u_2$ and $y_2\le v_2$.