In this paper we establish some fixed point results of multivalued α-admissible mappings in the framework of metric spaces. The mappings are assumed to satisfy certain rational type α−ψ-contractions. We support our main results with an example. We use Hausdorff distance in our theorems. We also study the stability of fixed point sets of above mentioned set valued contractions. By applications of the multivalued results we obtain certain fixed point theorems of singlevalued mappings.

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In this paper, we established a stability result for fixed point sets associated with a sequence of multivalued mappings which belong to class of functions obtained by a multivalued extension of certain generalized contraction mapping. Certain other aspects of these mappings are already studied in the existing literatures. We also construct an illustrative example.

Abstract. In this paper we establish that a pair of compatible mappings have unique common fixed point in metric and partial metric spaces respectively. The mappings are Suzuki type. We give examples to illustrate our results.

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