Rate of convergence of nonlinear integral operators for functions of bounded variation

CALCOLO ◽  
2008 ◽  
Vol 45 (2) ◽  
pp. 87-98 ◽  
Author(s):  
Harun Karsli ◽  
Vijay Gupta
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Integral Operators ◽  
Functions Of Bounded Variation ◽  
Nonlinear Integral Operators

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 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.

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.

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