Abstract. In the present paper, considering a recent technique which is used by Jleli and Samet [10] for fixed points of single-valued maps, we introduce a new concept of multivalued θ-contractions on metric spaces and prove that some of such mappings are multivalued weakly Picard operators on complete metric space. Finally, we give a nontrivial example to show that the class of multivalued θ-contractions is more general than multivalued contractions in the sense of Nadler [14] on complete metric spaces.
In this paper we show that on complete metric spaces the class of weakly Picard operators contains some operators which are more general than the class of almost contractions.
In the present paper, by introducing the P -contractivity of a multivalued mapping, we give a new class of multivalued weakly Picard operators on complete metric spaces and show that the class of multivalued contractions is a proper subset of this new class. We also give a nontrivial example showing this fact.
In this paper, by considering the concept of set-valued nonlinear P-contraction which is newly introduced, we present some new fixed point theorems for set-valued mappings on complete metric space. Then by considering a single-valued case we provide an existence and uniqueness result for a kind of second order two point boundary value problem.
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