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-distance and endowed with a graph. These results prepare a more general statement, since we apply the condition of orbitally-continuity of mapping instead of the condition of continuity, and consider cone metric spaces endowed with a graph instead of cone metric spaces.

In this article, applying the concept of a generalized c -distance in cone b -metric spaces over Banach algebra with a nonnormal solid cone therein, we establish several common fixed point theorems for two noncontinuous mappings satisfying the Han-Xu-type contraction. Our results are interesting, since they are not equivalent to former well-known results regarding a w t -distance in b -metric spaces while they contain recent results corresponding to a generalized c -distance in cone b -metric spaces.