Search results for "modulus of continuity"
showing 10 items of 35 documents
Estimates for the differences of positive linear operators and their derivatives
2019
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Oxur approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, and Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of the first modulus of continuity. In order to analyze the theoretical results in the last section, we consider some numerical examples.
On Functions of Integrable Mean Oscillation
2005
Given f 2 L1(T) we denote by wmo(f) the modulus of mean oscillation given by wmo(f)(t) = sup 0 0 such that Z 1 0 [wmo(f)(t)]p dt t Z 1 0 [who(f)(t)]p dt t Cp Z 1 0 [wmo(f)(t)]p dt t. -Oscar.Blasco@uv.es
Some approximation properties by a class of bivariate operators
2019
WOS: 000503431300041
A local notion of absolute continuity in IR^n
2005
We consider the notion of p, δ-absolute continuity for functions of several variables introduced in [2] and we investigate the validity of some basic properties that are shared by absolutely continuous functions in the sense of Maly. We introduce the class $δ−BV^p_loc(\Omega,IR^m)$ 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.
Modulus of continuity with respect to semigroups of analytic functions and applications
2016
Abstract Given a complex Banach space E , a semigroup of analytic functions ( φ t ) and an analytic function F : D → E we introduce the modulus w φ ( F , t ) = sup | z | 1 ‖ F ( φ t ( z ) ) − F ( z ) ‖ . We show that if 0 α ≤ 1 and F belongs to the vector-valued disc algebra A ( D , E ) , the Lipschitz condition M ∞ ( F ′ , r ) = O ( ( 1 − r ) 1 − α ) as r → 1 is equivalent to w φ ( F , t ) = O ( t α ) as t → 0 for any semigroup of analytic functions ( φ t ) , with φ t ( 0 ) = 0 and infinitesimal generator G , satisfying that φ t ′ and G belong to H ∞ ( D ) with sup 0 ≤ t ≤ 1 ‖ φ ′ ‖ ∞ ∞ , and in particular is equivalent to the condition ‖ F − F r ‖ A ( D , E ) = O ( ( 1 − r ) α ) as r …
On the continuity of discrete maximal operators in Sobolev spaces
2014
We investigate the continuity of discrete maximal operators in Sobolev space W 1;p (R n ). A counterexample is given as well as it is shown that the continuity follows under certain sucient assumptions. Especially, our research verifies that for the continuity in Sobolev spaces the role of the partition of the unity used in the construction of the maximal operator is very delicate.
Extremal length and Hölder continuity of conformal mappings
1986
Generalized Alomari functionals
2015
We consider a generalized form of certain integral inequalities given by Guessab, Schmeisser and Alomari. The trapezoidal, mid point, Simpson, Newton-Simpson rules are obtained as special cases. Also, inequalities for the generalized Alomari functional in terms of the $n$-th order modulus, $n=\overline{1,4}$, are given and applied to some known quadrature rules.