On statistical approximation of a general class of positive linear operators extended in q-calculus

Radu, Cristina

doi:10.1016/j.amc.2009.08.023

Cited by 23 publications

(20 citation statements)

References 12 publications

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“…by using the test functions .In addition, some related papers on this topic can be found in [33][34][35]. In this paper, we generalize the result of Boyanov and Veselinov by using the notion of statistical summability ( )( )…”

Section: Application To Approximation Theoremmentioning

confidence: 96%

Some results of weighted Norlund-Euler statistical convergence

Aljimi¹,

Hoxha²,

Loku³

2013

imf

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Section: Application To Approximation Theoremmentioning

confidence: 96%

Some results of weighted Norlund-Euler statistical convergence

Aljimi¹,

Hoxha²,

Loku³

2013

imf

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“…Recently, in [1], we introduced a q-generalization of the classical Baskakov operators. Radu [3] proposed generalized operators which include the slightly modified q Baskakov operators. For f ∈ C [0, ∞) , q > 0 and each positive integer n, the q-Baskakov operators (see [3]) are defined as…”

Section: Introduction and Notationsmentioning

confidence: 99%

On certain Durrmeyer type q Baskakov operators

Gupta

2010

Ann. Univ. Ferrara

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“…P r o o f. The proof is based on the limit lim n→∞ 2[n] q n (x − v n,q n (x)) = 1 and on the formula (12). If A n,q n (x), B n,q n (x), C n,q n (x), D n,q n (x) first, second, third and fourth terms of the formula (12), respectively, then…”

Section: Construction and Estimation Of Momentsmentioning

confidence: 99%

q-Szász operators which preserve x 2

Mahmudov

2013

Mathematica Slovaca

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ABSTRACT. In the present paper we construct q-Szász operators that preserve the third test function e 2 . Rate of global convergence is obtained in the frame of weighted spaces. Furthermore, we obtain a Voronovskaja type theorem for these operators. This sequence preserves the test functions e 0 , e 2 and V n (e 1 ; x) = r * n (x) holds. The goal of this article is to construct and investigate a variant of q-Szász-Mirakjan operators in the case q > 1, studied in [10], which preserve the functions e 0 and e 2 . Constructed operator has a better rate of convergence than the classical King type Szász-Mirakjan operators studied in [3].The paper is organized as follows. In Section 2, we give standard notations that will be used throughout the paper, introduce King type q-Szász operators and evaluate their moments. In Section 3, we study convergence properties of our operators for functions with polynomial growth. The main tool is a weighted modulus of smoothness. Furthemore we give a Voronovskaja-type asymptotic formula.

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On statistical approximation of a general class of positive linear operators extended in q-calculus

Cited by 23 publications

References 12 publications

Some results of weighted Norlund-Euler statistical convergence

Some results of weighted Norlund-Euler statistical convergence

On certain Durrmeyer type q Baskakov operators

q-Szász operators which preserve x 2

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