scholarly journals Rate of approximation of functions of bounded variation by modified Lupas operators

1991 ◽  
Vol 44 (2) ◽  
pp. 177-188 ◽  
Author(s):  
Wang Yuankwei ◽  
Guo Shunsheng
Keyword(s):  
Bounded Variation ◽  
Approximation Theorem ◽  
Functions Of Bounded Variation ◽  
Approximation Of Functions ◽  
Rate Of Approximation ◽  
Lupaş Operators

This paper discusses the rate of approximation of functions of bounded variation using the Modified Lupas operator. We obtain an approximation theorem and our estimate is essentially the best possible.

Approximation of functions of bounded variation by integrated Meyer-König and Zeller operators of finite type

2012 ◽  
Vol 49 (2) ◽  
pp. 254-268
Author(s):  
Tiberiu Trif
Keyword(s):  
Rate Of Convergence ◽  
Finite Type ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
Approximation Of Functions ◽  
Durrmeyer Operators

I. Gavrea and T. Trif [Rend. Circ. Mat. Palermo (2) Suppl. 76 (2005), 375–394] introduced a class of Meyer-König-Zeller-Durrmeyer operators “of finite type” and investigated the rate of convergence of these operators for continuous functions. In the present paper we study the approximation of functions of bounded variation by means of these operators.

scholarly journals Rate of approximation for the Bézier variant of Balazs Kantorovich operators

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Vijay Gupta ◽  
X. Zeng
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Rate Of Approximation ◽  
Kantorovich Operators ◽  
Bézier Variant

AbstractIn the present paper we study the Bézier variant of the well known Balazs-Kantorovich operators L n,α(f,x), α ≥ 1. We establish the rate of convergence for functions of bounded variation. For particular value α = 1, our main theorem completes a result due to Agratini [Math. Notes (Miskolc) 2 (2001), 3–10].

scholarly journals General family of exponential operators

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4043-4060
Author(s):  
Km. Lipi ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Error Estimation ◽  
Bounded Variation ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Approximation Of Functions ◽  
Direct Approximation ◽  
Derivatives Of

In this article, we deal with the approximation properties of Ismail-May operators [16] based on a non-negative real parameter ?. We provide some graphs and error estimation table for a numerical example depicting the convergence of our proposed operators. We further define the B?zier variant of these operators and give a direct approximation theorem using Ditizan-Totik modulus of smoothness and a Voronovoskaya type asymptotic theorem. We also study the error in approximation of functions having derivatives of bounded variation. Lastly, we introduce the bivariate generalization of Ismail May operators and estimate its rate of convergence for functions of Lipschitz class.

Approximation by Bézier variant of the Szász–Kantorovich operators in case α < 1

2010 ◽  
Vol 17 (2) ◽  
pp. 253-260
Author(s):  
Vijay Gupta ◽  
Xiao-Ming Zeng
Keyword(s):  
Bounded Variation ◽  
Convergence Theorem ◽  
Functions Of Bounded Variation ◽  
Approximation Properties ◽  
Approximation Of Functions ◽  
Type Approximation ◽  
Bounded Functions ◽  
Kantorovich Operators ◽  
Special Case ◽  
Bézier Variant

Abstract The present paper deals with the Bézier variant of the Szász–Kantorovich operator. Its approximation properties are studied. A convergence theorem of this type approximation operators for locally bounded functions is established, which subsumes the approximation of functions of bounded variation as a special case.

scholarly journals Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Error Bounds ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Dirichlet Kernel ◽  
Partial Sums ◽  
Functions Of Bounded Variation ◽  
Moduli Of Continuity ◽  
Fourier Approximation

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.

scholarly journals Some Bounds for the Complex Čebyšev Functional of Functions of Bounded Variation

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 990
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Functional Applications ◽  
Čebyšev Functional

In this paper, we provide several bounds for the modulus of the complex Čebyšev functional. Applications to the trapezoid and mid-point inequalities, that are symmetric inequalities, are also provided.

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