In this paper we prove a common fixed point theorem in fuzzy 2-metric space on six self-mappings using the concept of compatible of type (K) and Property (E.A.).
We construct a countable set \( S \) that possesses the essential properties of the real numbers: it is everywhere dense in \( \mathbb{R} \) and Dedekind complete, with no gaps. Each element of \( S \) is part of a unique triplet \(... more
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and... more
The aim of this paper is to obtain a common fixed point theorem for self mappings in complete fuzzy metric space by compactable of type (E). Our result generalizes and improves other similar results in literature [7].
The purpose of this article is to introducing the notion of an A-meter, as an operator valued distance mapping on a set X and investigating the theory of A-metric spaces, where A is a noncommutative C *-algebra. We demonstrate that each... more
For a mapping f : X → Y between metric spaces the function lipf : X → [0, ∞] defined by lipf (x) = lim inf r→0 diam f (B(x, r)) r is termed the lower scaled oscillation or little lip function. We prove that, given any positive integer d... more
A negative solution of Problem 188 posed by Max Eidelheit in the Scottish Book concerning superpositions of separately absolutely continuous functions is presented. We discuss here his and some related problems which have also negative... more
We show that middle interval Cantor sets of Hausdorff dimension 1 are minimal for quasisymmetric maps of a line. Combining this with a theorem of Wu we conclude that there are “rigid” subsets of a line whose every quasisymmetric image has... more
We show that if f : X → Y is a quasisymmetric mapping between Ahlfors regular spaces, then dimH f (E) ≤ dimH E for "almost every" bounded Ahlfors regular set E ⊆ X. If additionally, X and Y are Loewner spaces then dimHf (E) = dimH E for... more
In this paper we give several conditions for a space to be minimal for conformal dimension. We show that there are sets of zero length and conformal dimension 1 thus answering a question of Bishop and Tyson. Another sufficient condition... more
Let $B^{H}$ be a fractional Brownian motion in $\mathbb{R}^{d}$ of Hurst index $H\in\left(0,1\right)$ , $f\;:\;\left[0,1\right]\longrightarrow\mathbb{R}^{d}$ a Borel function and $A\subset\left[0,1\right]$ a Borel set. We provide... more
In this paper, the notion of S-metric spaces will be introduced. We present some fixed point theorems for two maps on complete S-metric spaces and an illustrative example is given for the single-valued case. By using the similar method as... more
Abstract. Lebesgue Measure plays an important role in defining width of area under some graphs of real-valued function while the domain lies in real number system accurately. Yet such measure fails to approximate the area under the graph... more
Abstract. For a complete measure space (X,Σ,µ), we give conditions which force Lp(X,µ), for 1 ≤ p < ∞, to be isometrically isomorphic to p(Γ) for some index set Γ which depends only on (X,µ). Also, we give some new characterizations... more
We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the α-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasipseudometric parts. This... more
We provide a permutation-invariant version of the Komlós' theorem for non-negative random variables. The proof is quite elementary in the sense that it did not use the Axiom of Choice, and was based on a recent result in [3].
In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth diffeomorphisms of S which preserve this Cantor set. When the... more
In this paper we study on contribution of fixed point theorem in Metric spaces and Quasi Metric spaces.
In this paper we study on contribution of fixed point theorem in Metric spaces and Quasi Metric spaces.
In this paper we make a survey of some recent developments of the theory of Sobolev spaces W 1,q (X, d, m), 1 < q < ∞, in metric measure spaces (X, d, m). In the final part of the paper we provide a new proof of the reflexivity of the... more
This note is dedicated to the study of the asymptotic behaviour of sets of finite perimeter over RCD(K, N) metric measure spaces. Our main result asserts existence of a Euclidean tangent half-space almost everywhere with respect to the... more
We introduce the setting of extended metric-topological measure spaces as a general "Wiener like" framework for optimal transport problems and nonsmooth metric analysis in infinite dimension. After a brief review of optimal transport... more
Motivated by recent developments on calculus in metric measure spaces (X, d, m), we prove a general duality principle between Fuglede's notion [15] of p-modulus for families of finite Borel measures in (X, d) and probability measures with... more
In this paper we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X, d, m) which is stable under measured Gromov-Hausdorff convergence and rules out Finsler geometries. It can be given in terms... more
We develop an axiomatic approach to the theory of Sobolev spaces on metric measure spaces and we show that this axiomatic construction covers the main known examples (Hajtasz Sobolev spaces, weighted Sobolev spaces, Upper-gradients, etc).... more
In this work, we are concerned with the study of the N-Lusin property in metric measure spaces. A map satisfies that property if sets of measure zero are mapped to sets of measure zero. We prove a new sufficient condition for the N-Lusin... more
We explore the theory of blocking duality pioneered by Fulkerson et al. in the context of $p$-modulus on networks. We formulate an analogue on networks to the theory of conjugate families in complex analysis. Also we draw a connection... more
In this paper we make a survey of some recent developments of the theory of Sobolev spaces W 1,q (X, d, m), 1 < q < ∞, in metric measure spaces (X, d, m). In the final part of the paper we provide a new proof of the reflexivity of the... more
Motivated by recent developments on calculus in metric measure spaces (X, d, m), we prove a general duality principle between Fuglede's notion [15] of p-modulus for families of finite Borel measures in (X, d) and probability measures with... more
We show that if f:X→ Y is a quasisymmetric mapping between Ahlfors regular spaces, then _H f(E)≤_H E for "almost every" bounded Ahlfors regular set E⊆ X. If additionally, X and Y are Loewner spaces then _H f(E)=_H E for... more
We show that if f : X → Y is a quasisymmetric mapping between Ahlfors regular spaces, then dimH f (E) ≤ dimH E for "almost every" bounded Ahlfors regular set E ⊆ X. If additionally, X and Y are Loewner spaces then dimHf (E) = dimH E for... more
In the thesis we discuss several questions related to the study of degenerate, possibly nonlinear PDEs of elliptic type. At first we discuss the equivalent conditions between the validity of weighted Poincaré inequalities, structure of... more
We consider infinite conformal iterated function systems on R d. We study the geometric structure of the limit set of such systems. Suppose this limit set intersects some l-dimensional C 1-submanifold with positive Hausdorff t-dimensional... more
We study a variational framework to compare shapes, modeled as Radon measures on R N , in order to quantify how they differ from isometric copies. To this purpose we discuss some notions of weak deformations termed reformations as well as... more
We consider the problem of finding on a given Euclidean domain Ω of dimension n ≥ 3 a complete conformally flat metric whose Schouten curvature A satisfies some equation of the form f (λ(−A)) = 1. This generalizes a problem considered by... more
This study examines whether family ownership control moderate the monitoring effectiveness of independent boards. Unlike developed countries such as the United Kingdom (UK) and the United States (US), which have a dispersed ownership... more
The problem of model checking procedural programs has fostered much research towards the definition of temporal logics for reasoning on context-free structures. The most notable of such results are temporal logics on Nested Words, such as... more
We study the connection between the p-Talagrand inequality and the q-logarithmic Sololev inequality for conjugate exponents p ≥ 2, q ≤ 2 in proper geodesic metric spaces. By means of a general Hamilton-Jacobi semigroup we prove that these... more
We develop a method using the modulus of curve families to study minimisation problems for the mean distortion functional in the class of finite distortion homeomorphisms. We apply our method to prove extremality of the spiral-stretch... more
This paper is concerned with a Delsarte-type extremal problem. Denote by $${\mathcal {P}}(G)$$ P ( G ) the set of positive definite continuous functions on a locally compact abelian group G. We consider the function class, which was... more
We generalize the classical Riesz convergence theorem to Lorentz spaces, i.e., if f, f1, f2, . . . ∈ L p,q such that fn → f (a.e. or in measure) and fn p,q → f p,q , then fn -f p,q → 0 as n → ∞.
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
This paper studies functions of bounded mean oscillation (BMO) on metric spaces equipped with a doubling measure. The main result gives characterizations for mappings that preserve BMO. This extends the corresponding Euclidean results by... more
We prove that the Abresch-Gromoll inequality holds on infinitesimally Hilbertian CD(K, N ) spaces in the same form as the one available on smooth Riemannian manifolds.
This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the... more
Continuing our investigation of quasiconformal mappings with convex potentials, we obtain a new characterization of quasiuniformly convex functions and improve our earlier results on the existence of quasiconformal mappings with... more
Using a real-life and imagined case studies, we demonstrate how a casual, informal political conversation on social media among ordinary citizens could be transformed into a policy discourse. It is done by deconstructing the logic of... more
We give a geometric characterization of extremal sets in p spaces (1 < p < ∞) that partially generalizes our previous result for such sets in Hilbert spaces. The main conjecture here is that there are no extremal sets in the case 1 < p < 2.
In this work, we address the convergence of the finite element approximation of the minimizer of the Freidlin-Wentzell (F-W) action functional for a non-gradient dynamical system perturbed by small noise. The F-W theory of large... more
The aim of the present paper is to extend Kantorovich's mass transport problem to the framework of upper/lower continuous capacities and to prove the cyclic monotonicity of the supports of optimal supermodular plans. As in the... more