On the rate of convergence of some integral operators for functions of bounded variation

2005 ◽  
Vol 42 (2) ◽  
pp. 235-252
Author(s):  
Octavian Agratini
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
General Class ◽  
Pointwise Convergence ◽  
Integral Operators ◽  
Positive Operators ◽  
Functions Of Bounded Variation ◽  
Linear Positive Operators ◽  
The One

In the present paper we define a general class Bn,a, a =1, of Durrmeyer-Bézier type of linear positive operators. Our main aim is to estimate the rate of pointwise convergence for functions f at those points x at which the one-sided limits f(x+) and f(x-) exist. As regards these functions defined on an interval J certain conditions are required. We discuss two distinct cases: Int (J)=(0,8) and Int (J)=(0,1).

scholarly journals Rate of convergence on Baskakov-Beta-Bezier operators for bounded variation functions

2002 ◽  
Vol 32 (8) ◽  
pp. 471-479 ◽  
Author(s):  
Vijay Gupta
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Open Problem ◽  
Positive Operators ◽  
Functions Of Bounded Variation ◽  
Linear Positive Operators ◽  
Bounded Variation Functions ◽  
Bézier Variant

We introduce a new sequence of linear positive operatorsBn,α(f,x), which is the Bezier variant of the well-known Baskakov Beta operators and estimate the rate of convergence ofBn,α(f,x)for functions of bounded variation. We also propose an open problem for the readers.

scholarly journals About Some Linear Operators

2007 ◽  
Vol 2007 ◽  
pp. 1-13
Author(s):  
Ovidiu T. Pop
Keyword(s):  
Rate Of Convergence ◽  
General Class ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Positive Operators ◽  
Linear Operators ◽  
Linear Positive Operators ◽  
Voronovskaja Type Theorem

Using the method of Jakimovski and Leviatan from their work in 1969, we construct a general class of linear positive operators. We study the convergence, the evaluation for the rate of convergence in terms of the first modulus of smoothness and we give a Voronovskaja-type theorem for these operators.

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

scholarly journals Rate of Convergence for Ibragimov-Gadjiev-Durrmeyer Operators

2017 ◽  
Vol 50 (1) ◽  
pp. 119-129 ◽  
Author(s):  
Tuncer Acar
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
General Class ◽  
Durrmeyer Operators ◽  
Special Cases ◽  
Derivatives Of

Abstract The present paper deals with the rate of convergence of the general class of Durrmeyer operators, which are generalization of Ibragimov-Gadjiev operators. The special cases of the operators include somewell known operators as particular cases viz. Szász-Mirakyan-Durrmeyer operators, Baskakov-Durrmeyer operators. Herewe estimate the rate of convergence of Ibragimov-Gadjiev-Durrmeyer operators for functions having derivatives of bounded variation.

On the regularity of one-sided fractional maximal functions

2018 ◽  
Vol 68 (5) ◽  
pp. 1097-1112 ◽  
Author(s):  
Feng Liu
Keyword(s):  
Bounded Variation ◽  
Maximal Functions ◽  
Continuous Case ◽  
Discrete Case ◽  
Maximal Operators ◽  
Functions Of Bounded Variation ◽  
Sharp Bounds ◽  
Regularity Properties ◽  
Natural Extensions ◽  
The One

Abstract In this paper we investigate the regularity properties of one-sided fractional maximal functions, both in continuous case and in discrete case. We prove that the one-sided fractional maximal operators $ \mathcal{M}_{\beta}^{+} $ and $ \mathcal{M}_{\beta}^{-} $ map $ W^{1,p}(\mathbb{R}) $ into $ W^{1,q}(\mathbb{R}) $ with 1 <p <∞, 0≤β<1/p and q=p/(1-pβ), boundedly and continuously. In addition, we also obtain the sharp bounds and continuity for the discrete one-sided fractional maximal operators $ M_{\beta}^{+} $ and $ M_{\beta}^{-} $ from $ \ell^{1}(\mathbb{Z}) $ to $ {\rm BV}(\mathbb{Z}) $. Here $ {\rm BV}(\mathbb{Z}) $ denotes the set of all functions of bounded variation defined on ℤ. The results we obtained represent significant and natural extensions of what was known previously.

scholarly journals A note on integral modification of the Meyer-König and Zeller operators

2003 ◽  
Vol 2003 (31) ◽  
pp. 2003-2009 ◽  
Author(s):  
Vijay Gupta ◽  
Niraj Kumar
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Present Note ◽  
Sharp Estimate ◽  
Functions Of Bounded Variation ◽  
Exact Bound ◽  
Bounded Variation Functions ◽  
Correct Estimate

Guo (1988) introduced the integral modification of Meyer-Kö nig and Zeller operatorsMˆnand studied the rate of convergence for functions of bounded variation. Gupta (1995) gave the sharp estimate for the operatorsMˆn. Zeng (1998) gave the exact bound and claimed to improve the results of Guo and Gupta, but there is a major mistake in the paper of Zeng. In the present note, we give the correct estimate for the rate of convergence on bounded variation functions.

Iterative combinations for Srivastava–Gupta operators

2020 ◽  
pp. 2150108
Author(s):  
Prerna Maheshwari Sharma
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Simultaneous Approximation ◽  
Higher Order ◽  
Positive Operators ◽  
Integral Type ◽  
Linear Positive Operators ◽  
General Family ◽  
Special Cases

In the year 2003, Srivastava–Gupta proposed a general family of linear positive operators, having some well-known operators as special cases. They investigated and established the rate of convergence of these operators for bounded variations. In the last decade for modified form of Srivastava–Gupta operators, several other generalizations also have been discussed. In this paper, we discuss the generalized modified Srivastava–Gupta operators considered in [H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37(12–13) (2003) 1307–1315], by using iterative combinations in ordinary and simultaneous approximation. We may have better approximation in higher order of modulus of continuity for these operators.

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