Search results for "Inuit"

Absolute continuity for Banach space valued mappings

2007

We consider the notion of p,λ,δ-absolute continuity for Banach space valued mappings introduced in [2] for real valued functions and for λ = 1. We investigate the validity of some basic properties that are shared by n, λ-absolutely continuous functions in the sense of Maly and Hencl. We introduce the class $δ-BV^p_{λ,loc}$ and we give a characterization of the functions belonging to this class.

Stancu–Schurer–Kantorovich operators based on q-integers

2015

The goal of this paper is to introduce and study q analogue of Stancu-Schurer-Kantorovich operators. A convergence theorem using the well known Bohman-Korovkin criterion is proven and the rate of convergence involving the modulus of continuity is established. The estimate of the rate of convergence by means of the Lipshitz function is considered. Furthermore, we obtained a Voronovskaja type result for these operators. Also, we investigate the statistical approximation properties of these operators using Korovkin type statistical approximation theorem.

Weighted Extrapolation Techniques for Finite Difference Methods on Complex Domains with Cartesian Meshes

2016

The design of numerical boundary conditions in high order schemes is a challenging problem that has been tackled in different ways depending on the nature of the problem and the scheme used to solve it numerically. In this paper we propose a technique to extrapolate the information from the computational domain to ghost cells for schemes with structured Cartesian Meshes on complex domains. This technique is based on the application of Lagrange interpolation with weighted filters for the detection of discontinuities that permits a data dependent extrapolation, with high order at smooth regions and essentially non oscillatory properties near discontinuities. This paper is a sequel of Baeza et…

Lipschitz conditions,b-arcwise connectedness and conformal mappings

1982

Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces

2006

MSC (2000) Primary: 31C35; Secondary: 31C45, 30C65 In this paper, we study the relationship between p-harmonic functions and absolutely minimizing Lipschitz extensions in the setting of a metric measure space (X, d, µ). In particular, we show that limits of p-harmonic functions (as p →∞ ) are necessarily the ∞-energy minimizers among the class of all Lipschitz functions with the same boundary data. Our research is motivated by the observation that while the p-harmonic functions in general depend on the underlying measure µ, in many cases their asymptotic limit as p →∞ turns out have a characterization that is independent of the measure. c

POINTS OF $\varepsilon$ -DIFFERENTIABILITY OF LIPSCHITZ FUNCTIONS FROM ${\bb R}^n$ TO ${\bb R}^{n-1}$

2002

This paper proves that for every Lipschitz function $f:{\bb R}^n\longrightarrow {\bb R}^m,\;m < n$ , there exists at least one point of $\varepsilon$ -differentiability of $f$ which is in the union of all $m$ -dimensional affine subspaces of the form $q_0+{\rm span}\{q_1,q_2,\ldots,q_m\},\;{\rm where}\;q_j(j=0,1,\ldots,m)$ are points in ${\bb R}^n$ with rational coordinates.

Fixed point results for F-contractive mappings of Hardy-Rogers-type

2014

Recently, Wardowski introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for self-mappings on complete metric spaces or complete ordered metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.

On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian

2012

Abstract This paper concerns the best Lipschitz extension problem for a discrete distance that counts the number of steps. We relate this absolutely minimizing Lipschitz extension with a discrete ∞-Laplacian problem, which arises as the dynamic programming formula for the value function of some e -tug-of-war games. As in the classical case, we obtain the absolutely minimizing Lipschitz extension of a datum f by taking the limit as p → ∞ in a nonlocal p -Laplacian problem.

Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets

2013

We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. We provide a metric area formula that applies to these mappings and more generally to all almost everywhere metrically differentiable Lipschitz mappings defined on a Carnot group. peerReviewed

Closedness and lower semicontinuity of positive sesquilinear forms

2009

The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.