scholarly journals One functional class of uniform convergence on a segment of truncated whittaker cardinal functions

2018 ◽  
Vol 1 (3) ◽  
Author(s):  
Alexandr Yurevich Trynin
Keyword(s):  
Uniform Convergence ◽  
Modulus Of Continuity ◽  
Functional Class ◽  
Whittaker Functions ◽  
Cardinal Functions

One functional class is described in terms of one-sided modulus of continuity and the modulus of positive (negative) variation on which thereis a uniform convergence of the truncated cardinal Whittaker functions.

Approximation by bivariate (p,q)-Baskakov–Kantorovich operators

2018 ◽  
Vol 25 (3) ◽  
pp. 397-407 ◽  
Author(s):  
Hatice Gul Ince Ilarslan ◽  
Tuncer Acar
Keyword(s):  
Uniform Convergence ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Properties ◽  
Korovkin Theorem ◽  
Central Moments ◽  
The Korovkin Theorem ◽  
Kantorovich Operators

AbstractThe present paper deals with the bivariate{(p,q)}-Baskakov–Kantorovich operators and their approximation properties. First we construct the operators and obtain some auxiliary results such as calculations of moments and central moments, etc. Our main results consist of uniform convergence of the operators via the Korovkin theorem and rate of convergence in terms of modulus of continuity.

scholarly journals On a Durrmeyer-type modification of the Exponential sampling series

2020 ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini
Keyword(s):  
Asymptotic Formula ◽  
Uniform Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Convergence Properties ◽  
Sampling Series ◽  
Quantitative Results ◽  
Uniformly Continuous

Abstract In this paper we introduce the exponential sampling Durrmeyer series. We discuss pointwise and uniform convergence properties and an asymptotic formula of Voronovskaja type. Quantitative results are given, using the usual modulus of continuity for uniformly continuous functions. Some examples are also described.

Approximation by max-product sampling Kantorovich operators with generalized kernels

2019 ◽  
pp. 1-26 ◽  
Author(s):  
Lucian Coroianu ◽  
Danilo Costarelli ◽  
Sorin G. Gal ◽  
Gianluca Vinti
Keyword(s):  
Uniform Convergence ◽  
Real Axis ◽  
Modulus Of Continuity ◽  
Higher Dimensions ◽  
Jackson Type ◽  
Convergence Properties ◽  
Type Estimate ◽  
Quantitative Estimates ◽  
Uniform Modulus Of Continuity ◽  
Kantorovich Operators

In a recent paper, for max-product sampling operators based on general kernels with bounded generalized absolute moments, we have obtained several pointwise and uniform convergence properties on bounded intervals or on the whole real axis, including a Jackson-type estimate in terms of the first uniform modulus of continuity. In this paper, first, we prove that for the Kantorovich variants of these max-product sampling operators, under the same assumptions on the kernels, these convergence properties remain valid. Here, we also establish the [Formula: see text] convergence, and quantitative estimates with respect to the [Formula: see text] norm, [Formula: see text]-functionals and [Formula: see text]-modulus of continuity as well. The results are tested on several examples of kernels and possible extensions to higher dimensions are suggested.

scholarly journals Some Fuzzy-Wavelet-Like Operators and Their Convergence

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
R. Ezzati ◽  
F. Mokhtarnejad ◽  
N. Hassasi
Keyword(s):  
Uniform Convergence ◽  
Real Number ◽  
Modulus Of Continuity ◽  
Scaling Function ◽  
New Method ◽  
Numerical Examples ◽  
Unit Operator ◽  
Function Of Two Variables

Firstly, we define some new fuzzy-wavelet-like operators via a real-valued scaling function to approximate the continuous fuzzy functions of one and two variables. Then, by using the modulus of continuity, we prove their pointwise and uniform convergence with rates to the fuzzy unit operatorI. Using these fuzzy-wavelet-like operators, we present some numerical examples to illustrate the applicability of the proposed method. Also, we give a new method to approximate the integration of continuous fuzzy real-number-valued function of two variables by using the fuzzy-wavelet-like operator.

scholarly journals The generalization of certain results for Szasz-Mirakjan-Schurer operators

2012 ◽  
Vol 21 (1) ◽  
pp. 79-85
Author(s):  
DAN MICLAUS ◽  
◽  
OVIDIU T. POP ◽  
Keyword(s):  
Uniform Convergence ◽  
Present Article ◽  
General Formula ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Order Of Approximation ◽  
Test Functions ◽  
Voronovskaja Type Theorem

The present article continues earlier research by authors, in order to reach two goals. Firstly, we give a general formula concerning calculation of the test functions by Szasz-Mirakjan-Schurer operators and secondly, we establish a Voronovskaja type theorem, the uniform convergence and the ´ order of approximation using the modulus of continuity for the same operators.

scholarly journals Uniform convergence rate for Birkhoff means of certain uniquely ergodic toral maps

2020 ◽  
pp. 1-26
Author(s):  
SILVIUS KLEIN ◽  
XIAO-CHUAN LIU ◽  
ALINE MELO
Keyword(s):  
Convergence Rate ◽  
Uniform Convergence ◽  
Modulus Of Continuity ◽  
Skew Product ◽  
Dimensional Torus ◽  
One Dimensional ◽  
Arithmetic Properties ◽  
Uniform Convergence Rate ◽  
The One ◽  
Uniquely Ergodic

Abstract We obtain estimates on the uniform convergence rate of the Birkhoff average of a continuous observable over torus translations and affine skew product toral transformations. The convergence rate depends explicitly on the modulus of continuity of the observable and on the arithmetic properties of the frequency defining the transformation. Furthermore, we show that for the one-dimensional torus translation, these estimates are nearly optimal.

scholarly journals Convergence of derivative of Szász type operators involving Charlier polynomials

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Purshottam N. Agrawal ◽  
Thakur Ashok K. Sinha ◽  
Avinash Sharma
Keyword(s):  
Uniform Convergence ◽  
Modulus Of Continuity ◽  
Convergence Theorem ◽  
Second Order ◽  
Order Derivative ◽  
Linear Combinations ◽  
Charlier Polynomials ◽  
First Order ◽  
Steklov Mean

<p style='text-indent:20px;'>The paper deals with the approximation of first order derivative of a function by the first order derivative of Szász-type operators based on Charlier polynomials introduced by Varma and Taşdelen [<xref ref-type="bibr" rid="b20">20</xref>]. The uniform convergence theorem, Voronovskaja type asymptotic theorem and an estimate of error in terms of the second order modulus of continuity of the derivative of the function are investigated. Further, it is shown that linear combinations of the derivative of the above operators converge to the derivative of function at a faster rate. Finally, an estimate of error in the approximation is obtained in terms of the <inline-formula><tex-math id="M1">\begin{document}$ (2k+2)th $\end{document}</tex-math></inline-formula> order modulus of continuity using Steklov mean.</p>

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