Geodesic
Common fixed points of Greguš type multi-valued mappings
Archivum mathematicum, Tome 38 (2002) no. 1, pp. 37-47

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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 Greguš 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.
Classification : 47H04, 47H10, 54H25
Keywords: common fixed points; $\delta $-compatible mappings; sub-compatible mappings; complete convex metric spaces 
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Rashwan, R. A.; Ahmed, Magdy A. Common fixed points of Greguš type multi-valued mappings. Archivum mathematicum, Tome 38 (2002) no. 1, pp. 37-47. http://geodesic.mathdoc.fr/item/ARM_2002__38_1_a3/