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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 [11] (Theorem B below) and Jungck [16] are thereby obtained. An example is given to support our extension.
AMSclassification. 54H25.
Keywords. Common fixed points, $\delta$-compatible mappings, sub-compatible mappings, complete convex metric spaces.