Abstract. This work is considered as a continuation of [19,20,24]. The concepts of $\delta$-compatibility and sub-compatibility of Li-Shan [19, 20] between a set-valued mapping and a single-valued mapping are used to establish some common fixed point theorems of Gregu\v s type under a $\phi$-type contraction on convex metric spaces. Extensions of known results, especially theorems by Fisher and Sessa  (Theorem B below) and Jungck  are thereby obtained. An example is given to support our extension.
Keywords. Common fixed points, $\delta$-compatible mappings, sub-compatible mappings, complete convex metric spaces.