In this paper, we extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mapping and many fixed point theorems for multivalued mappings. © 2012 Elsevier Ltd. All rights reserved.

The onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system. A recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single-valued ...

Some results regarding the existence of a fixed point for a multivalued non-expansive mapping defined on an unbounded subset of a reflexive Banach space are established.

In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditi...

* Correspondence: [email protected] Department of Mathematics, Ataturk University, Erzurum 25240, Turkey Full list of author information is available at the end of the article Abstract In this article, we first give a multivalued version of an iteration scheme of Agarwal et al. We use an idea due to Shahzad and Zegeye which removes a “strong condition” on the mapping involved in the ite...

In this paper, we introduce two new concepts of Feng-Liu type multivalued contraction mapping and cyclic mapping. Then, obtain some best proximity point results for such mappings on partial metric spaces by considering Feng-Liu's technique. Finally, provide examples to show the effectiveness our results.

In this short note we show that the outer norm of a sublinear mapping F, acting between Banach spaces X and Y and with domF = X, is finite only if F is single-valued. This implies in particular that for a sublinear multivalued mapping the inner and the outer norms cannot be finite simultaneously. AMS 2000 Subject Classification: 49J53, 47H04, 54C60.

In this paper, we establish some existence of fixed-point results for asymptotically regular multivalued mappings satisfying Kannan-type contractive condition without assuming compactness the underlying metric space or continuity mapping.

The aim of this note is twofold. First, we prove an analogue of the wellknownRobinson–Ursescu Theorem on the relative openness with a linear rate (restrictive metric regularity) of a multivalued mapping. Second, we prove a generalization of Graves Open Mapping Theorem for a class of mappings which can be approximated at a reference point by a bunch of linear mappings. The approximated non-linea...

In this paper, we introduce a new concept of KW-type ?-contraction mixed multivalued mapping. After that, obtain some fixed point results for both and single valued mappings Finally, provide noteworth example to show the effectiveness our result.