Fixed point results for Hardy–Rogers type contractions with respect to a $c$-distance in graphical cone metric spaces

The aim of this paper is to prove some existence and uniqueness results of the fixed points for Hardy–Rogers type contraction in cone metric spaces associated with a $c$-distance and endowed with a graph. These results prepare a more general statement, since we apply the condition of orbitally $G$-continuity of mapping instead of the condition of continuity, and consider cone metric spaces endowed with a graph instead of cone metric spaces.