Rate of convergence for Szasz–Mirakyan–Durrmeyer operators with derivatives of bounded variation

Gupta, Mridul Kumar; Beniwal, Man Singh; Goel, Prachi

doi:10.1016/j.amc.2007.10.036

Cited by 13 publications

(7 citation statements)

References 3 publications

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“…We refer the reader to some of the related papers (cf. [8, 9, 16–20] and [21] etc.). Let be the class of all functions in having a derivative which is locally of bounded variation on .…”

Section: Resultsmentioning

confidence: 99%

Szász-Durrmeyer operators involving Boas-Buck polynomials of blending type

2017

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The present paper introduces the Szász-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. Anal. 2012:680340, 2012). We establish the moments of the operator and a Voronvskaja type asymptotic theorem and then proceed to studying the convergence of the operators with the help of Lipschitz type space and weighted modulus of continuity. Next, we obtain a direct approximation theorem with the aid of unified Ditzian-Totik modulus of smoothness. Furthermore, we study the approximation of functions whose derivatives are locally of bounded variation.

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“…We refer the reader to some of the related papers (cf. [8, 9, 16–20] and [21] etc.). Let be the class of all functions in having a derivative which is locally of bounded variation on .…”

Section: Resultsmentioning

confidence: 99%

Szász-Durrmeyer operators involving Boas-Buck polynomials of blending type

2017

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“…Many mathematicians played an important role to contribute their research in this field and described their views regarding the rate of convergence of the various operators for function of bounded variation and for derivative of function of bounded variation. We refer to reader for more contributions in this area [22,24,27,28,34,35].…”

Section: Rate Of Convergence By Means Of Function Of Bounded Variationmentioning

confidence: 99%

Approximations on Stancu variant of Szasz-Mirakjan-Kantorovich type operators

Yadav,

Meher,

Mishra

2019

Preprint

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The present article deals with the approximation properties of modification of Stancu variant of the Szász-Mirakjan Kantorovich type operators. The order of approximation is determined in the term of modulus of continuity and second order of smoothness. Also in same section, we establish the rate of convergence in the Lipschit's sapce. A relation is derived by means of Peetre-K functional for the rate of convergence and some direct results are discussed. Asymptotic formula is derived for the said operators to check the asymptotic behavior. Some convergence properties are discussed in weighted spaces using weight function. Moreover, using the weighted modulus of continuity, Quantitative Voronovskaya type and Grüss Voronovskaya-type theorem are obtained. Here we study the rate of convergence of the said operators in terms of functions with derivative of bounded variations. At last, the graphical representations and table of numerical errors are given and a comparison takes place in the support of result.

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“…Shaw et al [ 32 ] obtained the rates for approximation of functions of bounded variation and for functions with derivatives of bounded variation by positive linear operators. Many mathematicians studied in this direction and their work pertaining to this area is described in the papers [ 14 , 26 , 33 – 38 ] etc.…”

Section: Weighted Approximationmentioning

confidence: 99%

Rate of convergence by Kantorovich-Szász type operators based on Brenke type polynomials

2017

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The present paper deals with the approximation properties of the univariate operators which are the generalization of the Kantorovich-Szász type operators involving Brenke type polynomials. We investigate the order of convergence by using Peetre’s K-functional and the Ditzian-Totik modulus of smoothness and study the degree of approximation of the univariate operators for continuous functions in a Lipschitz space, a Lipschitz type maximal function and a weighted space. The rate of approximation of functions having derivatives equivalent with a function of bounded variation is also obtained.

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Rate of convergence for Szasz–Mirakyan–Durrmeyer operators with derivatives of bounded variation

Cited by 13 publications

References 3 publications

Szász-Durrmeyer operators involving Boas-Buck polynomials of blending type

Szász-Durrmeyer operators involving Boas-Buck polynomials of blending type

Approximations on Stancu variant of Szasz-Mirakjan-Kantorovich type operators

Rate of convergence by Kantorovich-Szász type operators based on Brenke type polynomials

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