‎recently‎, ‎hussain et al.‎, ‎discussed the concept of $wt$-distance on a‎ ‎metric type space‎. ‎in this paper‎, ‎we prove some fixed‎ ‎point theorems for classes of contractive type multi-valued operators‎, ‎by using $wt$-distances in the setting of a complete metric type space‎. ‎these results generalize a result of feng and liu on multi-valued operators.

The aim of the present paper is to prove that the family of all closed nonempty subsets of a complete probabilistic metric space L is complete with respect to the probabilistic Pompeiu-Hausdorff metric H . The same is true for the families of all closed bounded, respectively compact, nonempty subsets of L. If L is a complete random normed space in the sense of Šerstnev, then the family of all n...

This paper recalls the work of D. Pompeiu who introduced the notion of set distance in his thesis published one century ago. The notion was further studied by F. Hausdorff, C. Kuratowski who acknowledged in their books the contribution of Pompeiu and it is frequently called the Hausdorff distance. keywords: Hausdorff distance, Hausdorff-Pompeiu distance, Pompeiu functions, Pompeiu conjecture, S...

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...

The aim of this paper is to continue the research work that we have done in a previous paper published in this journal see Mihail andMiculescu, 2008 . We introduce the notion of GIFS, which is a family of functions f1, . . . , fn : X → X, where X, d is a complete metric space in the above mentioned paper the case when X, d is a compact metric space was studied andm,n ∈ N. In case that the funct...

Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzuki-type multifunctions.  The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach ...

The applications of non-zero self distance function have recently been discovered in both symmetric and asymmetric spaces. With respect to invariant point results, the available literature reveals that idea has only examined for crisp mappings either or Hence, aim this paper is introduce notion points non-crisp set-valued metric-like To effect, technique κ-contraction Feng-Liu’s approach are co...

Many optimization problems can be reformulated as best approximation problems with respect to an appropriate norm. Their solutions are thus given by projection operators. It follows that projection operators play a key role in several areas, such as mechanics, minimization algorithms, variational inequalities, complementary problems. Thus, it is of interest to study the properties of such opera...

Let Ξ(H) denote the set of all nonzero closed convex cones in a finite dimensional Hilbert space H. Consider this set equipped with the bounded Pompeiu-Hausdorff metric δ. The collection of all pointed cones forms an open set in the metric space (Ξ(H), δ). One possible way of measuring the degree of pointedness of a cone K is by evaluating the distance from K to the set of all nonpointed cones....