Abstract:In this paper, inspired by the concept of b-metric space, we introduce the concept of extended b-metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our results extend/generalize many pre-existing results in literature.

We define the property (E.A) for single-valued and multivalued mappings and introduce the notion of T -weak commutativity for a hybrid pair (f, T ) of single-valued and multivalued maps. We obtain some coincidence and fixed point theorems for this class of maps and derive, as application, an approximation theorem.  2004 Elsevier Inc. All rights reserved.

An existence theorem for Volterra-type integral inclusion is establish in b-metric spaces. We first introduce two new F-contractions of Hardy-Rogers type and then establish fixed point theorems for these contractions in the setting of b-metric spaces. Finally, we apply our fixed point theorem to prove the existence theorem for Volterra-type integral inclusion. We also provide an example to show that our fixed point theorem is a proper generalization of a recent fixed point theorem by Cosentino et al.

No abstract

In this paper, we introduce the notion of (α, ψ, ξ )-contractive multivalued mappings to generalize and extend the notion of α-ψ-contractive mappings to closed valued multifunctions. We investigate the existence of fixed points for such mappings. We also construct an example to show that our result is more general than the results of α-ψ-contractive closed valued multifunctions. MSC: 47H10; 54H25

We extend the notions ofα-ψ-proximal contraction andα-proximal admissibility to multivalued maps and then using these notions we obtain some best proximity point theorems for multivalued mappings. Our results extend some recent results by Jleli and those contained therein. Some examples are constructed to show the generality of our results.

No abstract

In this paper, we introduce the notions of α-F-contractions, by combining the notions of α-ψcontraction and F-contraction. Using our new notions we obtain some fixed point theorems for multivalued mappings. As an application we establish an existence theorem for integral equations. An example is also constructed to show an importance of our results.