scholarly journals Rate of convergence of beta operators of second kind for functions with derivatives of bounded variation

2005 ◽  
Vol 2005 (23) ◽  
pp. 3827-3833 ◽  
Author(s):  
Vijay Gupta ◽  
Ulrich Abel ◽  
Mircea Ivan
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Function Of Bounded Variation ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of

We study the approximation properties of beta operators of second kind. We obtain the rate of convergence of these operators for absolutely continuous functions having a derivative equivalent to a function of bounded variation.

scholarly journals Approximation by generalized positive linear Kantorovich operators

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4353-4368 ◽  
Author(s):  
Minakshi Dhamija ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Continuous Functions ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of ◽  
Kantorovich Operators

In the present article, we introduce generalized positive linear-Kantorovich operators depending on P?lya-Eggenberger distribution (PED) as well as inverse P?lya-Eggenberger distribution (IPED) and for these operators, we study some approximation properties like local approximation theorem, weighted approximation and estimation of rate of convergence for absolutely continuous functions having derivatives of bounded variation.

scholarly journals Approximation properties of a new generalized Bernstein-Kantorovich operators

2018 ◽  
Vol 214 ◽  
pp. 02003
Author(s):  
Bo-yong Lian
Keyword(s):  
Rate Of Convergence ◽  
Continuous Functions ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Kantorovich Operators

By means of construction of suitable functions and the method of Bojanic-Cheng, the author gives the rate of convergence of a new generalized Bernstein-Kantorovich operators for some absolutely continuous functions.

scholarly journals The Nemitskij operator on Lipk-type and BVk-type spaces

2013 ◽  
Vol 46 (3) ◽  
Author(s):  
José Giménez ◽  
Lorena López ◽  
N. Merentes
Keyword(s):  
Bounded Variation ◽  
Continuous Functions ◽  
Function Spaces ◽  
Compact Interval ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Type Spaces

AbstractIn this paper, we discuss and present various results about acting and boundedness conditions of the autonomous Nemitskij operator on certain function spaces related to the space of all real valued Lipschitz (of bounded variation, absolutely continuous) functions defined on a compact interval of ℝ. We obtain a result concerning the integrability of products of the form

scholarly journals Perturbed Companions of Ostrowski’s Inequality for Absolutely Continuous Functions (I)

2016 ◽  
Vol 54 (1) ◽  
pp. 119-138
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Bounded Variation ◽  
Continuous Functions ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Ostrowski’S Inequality

Abstract Perturbed companions of Ostrowski’s inequality for absolutely continuous functions whose derivatives are either bounded or of bounded variation and applications are given.

First order absolute moment of Meyer-König and Zeller operators and their approximation for some absolutely continuous functions

2011 ◽  
Vol 61 (4) ◽  
Author(s):  
Xiao-Ming Zeng ◽  
Fuhua Cheng
Keyword(s):  
Rate Of Convergence ◽  
Sharp Estimate ◽  
Continuous Functions ◽  
Absolute Moment ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
First Order

AbstractA sharp estimate is given for the first order absolute moment of Meyer-König and Zeller operators M n. This estimate is then used to prove convergence of approximation of a class of absolutely continuous functions by the operators M n. The condition considered here is weaker than the condition considered in a previous paper and the rate of convergence we obtain is asymptotically the best possible.

Absolute Continuity of Some Vector Functions and Measures

1972 ◽  
Vol 24 (5) ◽  
pp. 737-746 ◽  
Author(s):  
William J. Knight
Keyword(s):  
Bounded Variation ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Continuous Point ◽  
Uniform Boundedness Principle ◽  
Vector Valued Functions ◽  
Analogous Theorem ◽  
Vector Valued

In the theory of vector valued functions there is a theorem which states that if a function from a compact interval I into a normed linear space X is of weak bounded variation, then it is of bounded variation. The proof uses in a straightforward way the Uniform Boundedness Principle (see [2, p. 60]). The present paper grew from the question of whether an analogous theorem holds for absolutely continuous functions. The answer is in the negative, and an example will be given (Theorem 7). But it will also be shown that if X is weakly sequentially complete (e.g. an Lp space, 1 ≦ p < ∞ ), then a weakly absolutely continuous point function from / into X is absolutely continuous. The method of proof involves the construction of a countably additive set function in the standard Lebesgue-Stieltjes fashion.The paper is divided into three parts. In Section 1 extensions of finitely additive, absolutely continuous set functions are carried out in an abstract setting. Section 2 applies this to vector valued (point) functions on the real line.

scholarly journals VARIATION PROBLEM CONTAINING SECOND DERIVATIVES OF UNKNOWN FUNCTIONS

2021 ◽  
Vol 6 (1(34)) ◽  
pp. 30-42
Author(s):  
Misraddin Allahverdi oglu Sadigov
Keyword(s):  
Variational Problem ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Necessary Condition ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Variation Problem ◽  
Second Derivatives ◽  
Necessary And Sufficient ◽  
Derivatives Of

The property subdifferential of an integral and terminal functional in a space of the type of absolutely continuous functions is studied. Necessary and sufficient conditions for an extremum for a variational problem containing the second derivatives of unknown functions are obtained. With the help of the subdifferential introduced by the author, a nonconvex generalized variational problem containing the second derivatives of unknown functions is considered, and the necessary condition for an extremum is obtained.

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