## Tbilisi Mathematical Journal

### Some approximation properties of generalized integral type operators

#### 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
Accepted: 28 December 2017
First available in Project Euclid: 21 April 2018

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

#### 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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