Tbilisi Mathematical Journal

Some approximation properties of generalized integral type operators

Alok Kumar and Vandana

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Abstract

In this paper we introduce and study the Stancu type generalization of the integral type operators defined in (1.1). First, we obtain the moments of the operators and then prove the Voronovskaja type asymptotic theorem and basic convergence theorem. Next, the rate of convergence and weighted approximation for the above operators are discussed. Then, weighted $L_p$-approximation and pointwise estimates are studied. Further, we study the $A$-statistical convergence of these operators. Lastly, we give better estimations of the above operators using King type approach.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 1 (2018), 99-116.

Dates
Received: 24 September 2017
Accepted: 28 December 2017
First available in Project Euclid: 21 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1524276033

Digital Object Identifier
doi:10.2478/tmj-2018-0007

Mathematical Reviews number (MathSciNet)
MR3770041

Zentralblatt MATH identifier
1384.41013

Subjects
Primary: 41A25: Rate of convergence, degree of approximation
Secondary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 40A35: Ideal and statistical convergence [See also 40G15]

Keywords
Voronovskaja-type theorem integral type operators rate of convergence modulus of continuity weighted $L_p$-approximation

Citation

Kumar, Alok; Vandana. Some approximation properties of generalized integral type operators. Tbilisi Math. J. 11 (2018), no. 1, 99--116. doi:10.2478/tmj-2018-0007. https://projecteuclid.org/euclid.tbilisi/1524276033


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