Multivalued fixed point results in cone metric spaces

Fuzzy b-Metric Spaces: Fixed Point Results for ψ-Contraction Correspondences and Their Application

“…In this paper we define the ψ-contractive and monotone ψ-contractive correspondence and prove some results for the existence of fixed points for these contractive conditions in "fuzzy b-metric spaces", where ψ ∈ Ψ and Ψ consists of all the functions ψ : R + ∪ {0} → R + ∪ {0} being continuous, nondecreasing and ψ(1) = 1. It is important to mention that several researchers have obtained fixed points of correspondence satisfying the contractive conditions via the Hausdorff distance [38][39][40][41][42][43]. We improve Theorem 1 in a short and comprehensive way and obtain the result without using the Hausdorff distance.…”

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.…”

Fixed point theorems for set-valued mappings on TVS-cone metric spaces

“…Notice that for each δ ∈ K + (E) and x ∈ E, |δx| δ|x|. Some authors such as [4,5,9,12,15] define k-contraction as a set-valued mapping T : X → B(X) satisfying kd(x, y) ∈ s(T x, T y), for all x, y ∈ X.…”