Preface In this monograph various notions related to metric spaces are considered, including Hausdorff-type measures and dimensions, Lipschitz mappings, and the Hausdorff distance between nonempty closed and bounded subsets of a metric space. Some familiarity with basic topics in analysis such as Riemann integrals, open and closed sets, and continuous functions is assumed, as in [60, 100, 187],...

Preface In this monograph various notions related to metric spaces are considered, including Hausdorff-type measures and dimensions, Lipschitz mappings, and the Hausdorff distance between nonempty closed and bounded subsets of a metric space. Some familiarity with basic topics in analysis such as Riemann integrals, open and closed sets, and continuous functions is assumed, as in [50, 88, 160], ...

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...

In this paper, we introduce a new concept of fuzzy generalizedcontraction and give a fixed point result for such mappings in the setting of fuzzy M-complete metric spaces. We also give an affirmative partial answer to a question posed by Wardowski [D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Set Syst., {bf 222}(2013), 108-114].Some examples are also g...

In recent years, q-rung orthopair fuzzy sets (q-ROFSs), a novel and rigorous generalization of the set (FS) coined by Yager in 2017, have been used to manage inexplicit indefinite information daily life with high precision greater accuracy than intuitionistic (IFSs) Pythagorean (PFSs). The characterization measure similarity between q-ROFSs is important, as they applications different areas, in...

In this paper, we first consider the disjoint union of two fuzzy metric spaces and non-existence of fuzzy contractive maps. We prove that there exists a natural fuzzy metric on the disjoint union of two fuzzy metric spaces. We also show that there is a fuzzy metric space which does not admit any fuzzy contractive map. Second, we introduce the notion of a fuzzy diameter for fuzzy metric spaces a...

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...

The Gromov-Hausdorff distance provides a metric on the set of isometry classes of compact metric spaces. Unfortunately, computing this metric directly is believed to be computationally intractable. Motivated by applications in shape matching and point-cloud comparison, we study a semidefinite programming relaxation of the Gromov-Hausdorff metric. This relaxation can be computed in polynomial ti...

Binayak et al in [1] proved a fixed point of generalized Kannan type-mappings in generalized Menger spaces. In this paper we extend gen- eralized Kannan-type mappings in generalized fuzzy metric spaces. Then we prove a fixed point theorem of this kind of mapping in generalized fuzzy metric spaces. Finally we present an example of our main result.

Gromov-Hausdorff convergence is an important tool in comparison Riemannian geometry. Given a sequence of Riemannian manifolds of dimension n with Ricci curvature bounded from below, Gromov’s precompactness theorem says that a subsequence will converge in the pointed Gromov-Hausdorff topology to a length space [G-99, Section 5A]. If the sequence has bounded sectional curvature, then the limit wi...