Results 11 to 20 of about 4,785 (285)

MODIFIED MODULUS OF SMOOTHNESS AND APPROXIMATION IN WEIGHTED LORENTZ SPACES BY BOREL AND EULER MEANS [PDF]

Проблемы анализа, 2020
Using one-sided Steklov means, we introduce a new modulus of smoothness in weighted Lorentz spaces. The direct and inverse approximation theorem for this modulus of smoothness are proved.
S. S. Volosivets
doaj   +2 more sources

A New Modulus of Smoothness for Uniform Approximation [PDF]

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences, 2018
The estimates of best approximation using classical modulus of smoothness is not uniform. Also we sometimes need to improve the degree of best approximation near the end points. Thus we need to improve this classical modulus of smoothness. Here we define a new modulus of smoothness to achieve uniform estimates of  best approximation and an improvement ...
Bhaya, Eman Samir, Hussein, Bushra Khudhair   +1 more
openaire   +4 more sources

Modulus of smoothness and theorems concerning approximation on compact groups [PDF]

International Journal of Mathematics and Mathematical Sciences, 2003
We consider the generalized shift operator defined by (Shuf)(g)=∫Gf(tut−1g)dt on a compact group G, and by using this operator, we define “spherical” modulus of smoothness. So, we prove Stechkin and Jackson-type theorems.
H. Vaezi, S. F. Rzaev
doaj   +2 more sources

Some Modulus and Normal Structure in Banach Space [PDF]

Journal of Inequalities and Applications, 2009
We present some sufficient conditions for which a Banach space X has normal structure in terms of the modulus of U-convexity, modulus of W∗-convexity, and the coefficient R(1,X), which generalized some well-known results.
Zhanfei Zuo, Yunan Cui
doaj   +3 more sources

Characterization of Best Algebraic Approximation by an Algebraic Modulus of Smoothness [PDF]

Journal of Approximation Theory, 1997
Denoting by \( x \oplus h \) the weighted addition given by \( x \oplus h = x \sqrt{1-h^2} + \sqrt{1-x^2}h, \forall x, h \in [-1, 1], \) the author considers the difference operator of \( r\) th order of the function \( f: [-1, 1] \rightarrow \mathbb{R}, \) defined by \( \Delta_h^r f = (\Delta_h\circ\ldots\circ\Delta_h)(f), \) (\(r \) times) where \( (\
Felten, Michael
openaire   +2 more sources

Best trigonometric approximation and modulus of smoothness of functions in weighted grand Lebesgue spaces [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2019
In this work, first of all, Lpw),Ө (T) weighted grand Lebesgue spaces and Muckenhoupt weights is defined. The information about properties of these spaces is given. Let Tn be the trigonometric polynomial of best approximation.
Sadulla Z. Jafarov
doaj   +3 more sources

Towards the best constant in front of the Ditzian-Totik modulus of smoothness [PDF]

Journal of Inequalities and Applications, 2016
We give accurate estimates for the constants K ( A ( I ) , n , x ) = sup f ∈ A ( I ) | L n f ( x ) − f ( x ) | ω σ 2 ( f ; 1 / n ) , x ∈ I , n = 1 , 2 , … , $$ K\bigl(\mathcal{A}(I), n, x\bigr)=\sup_{f\in\mathcal{A}(I)}\frac{|L_{n} f(x)-f(x)|}{\omega_ ...
José A Adell, Alberto Lekuona
doaj   +3 more sources

Derivatives of Multivariate Bernstein Operators and Smoothness with Jacobi Weights [PDF]

Journal of Applied Mathematics, 2012
Using the modulus of smoothness, directional derivatives of multivariate Bernstein operators with weights are characterized. The obtained results partly generalize the corresponding ones for multivariate Bernstein operators without weights.
Jianjun Wang, Zuoxiang Peng, Shukai Duan, Jia Jing   +3 more
doaj   +2 more sources

Global smoothness and approximation by generalized discrete singular operators [PDF]

Journal of Numerical Analysis and Approximation Theory, 2014
In this article we continue with the study of generalized discrete singular operators over the real line regarding their simultaneous global smoothness preservation property with respect to \(L_{p}\) norm for \( 1\leq p\leq \infty ,\) by involving ...
George A. Anastassiou, Merve Kester
doaj   +4 more sources

The second order modulus revisited: remarks, applications, problems [PDF]

Journal of Numerical Analysis and Approximation Theory
Several questions concerning the second order modulus of smoothness are addressed in this note. The central part is a refined analysis of a construction of certain smooth functions by Zhuk and its application to several problems in approximation theory,
Heiner Gonska, Ralitza K. Kovacheva
doaj   +3 more sources