Multivalued fixed point theorems in cone b-metric spaces

Abstract

In this paper we extend the Banach contraction for multivalued mappings in a cone b-metric space without the assumption of normality on cones and generalize some attractive results in literature. MSC: 47H10; 54H25

A noncompactness measure for tvs-metric cone spaces and some applications

“…As in [5,6,10,22,28], we say T is a contraction whenever k < 1. In this work, the set-valued mapping T is said to be non-expansive, whenever (4.1) is satisfied with k = 1.…”

“…Indeed, these authors introduced an example of contraction, on a cone metric space, which is not contraction in a standard metric space. As in [1,3,4,6,10,22,24,29,31], this has led some authors to publish numerous papers both on fixed point theory as on properties of cone metric spaces. However, it has not been paid attention enough to the topology of these spaces.…”

EXISTENCE OF FIXED POINTS OF SET-VALUED MAPPINGS IN b-METRIC SPACES

“…Following these initial papers, the existence and the uniqueness of (common) fixed points for the classes of both singlevalued and multivalued operators in the setting of (generalized) b-metric spaces have been investigated extensively, (see e.g. [1,3,4,5,9,13,14,15,16,24,26,27] and related references therein. )…”

Fixed point results for multivalued mappings on a sequence in a closed ball with applications

“…Nadler [20], introduced a study of fixed point theorems involving multivalued mappings (see also [8,9]). The existence of fixed points of α-admissible mappings in complete metric spaces has been studied by several researchers (see [18,23,27]).…”