Common fixed points of single-valued and multivalued maps

The fixed points theorems for Rhoades-type contraction mapping were investigated by many authors [1, 5, 8, 10, 13, 16, 22] and the more results on this fields can be found in [2, 4, 9, 11, 15, 23]. Hybrid fixed point theory for nonlinear single-valued and multivalued maps is a new development in the domain of contraction-type multivalued theory (see [3, 7, 10, 12, 14, 17, 18, 20] and references therein). In 1998, Jungck and Rhoades [12] introduced the notion of weak compatibility to the setting of single-valued and multivalued maps. In [21], Singh and Mishra introduced the notion of (IT)-commutativity for hybrid pair of single-valued and multivalued maps which need not be weakly compatible. Recently, Aamri and El Moutawakil [1] defined a property (EA) for self-maps which contained the class of noncompatible maps. More recently, Kamran [13] extended the property (EA) for a hybrid pair of singleand multivalued maps and generalized the notion of (IT)-commutativity for such pair.