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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. [ABSTRACT FROM AUTHOR]

In this paper, first we introduce two new types almost contractions on quasi metric space named as almost (α, Fd)-contraction of type (x) and of type (y). Then, taking into account both left and right completeness of quasi metric space, we present some fixed point results for these contractions. We also provide some illustrative and comparative examples. [ABSTRACT FROM AUTHOR]

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 φ-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 φ-contractions is more general than multivalued contractions in the sense of Nadler [14] on complete metric spaces. [ABSTRACT FROM AUTHOR]