Related fixed points for set valued mappings on two metric spaces.

Fisher, Brian; Türkoḡlu, Duran

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Common fixed points of Greguš type multi-valued mappings

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This work is considered as a continuation of [19,20,24]. The concepts of $δ$ -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 $φ$ -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. ...