On a special class of modified integral operators preserving some exponential functions

Gümrah Uysal

doi:10.3934/mfc.2021044

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2023, Volume 6, Issue 1: 78-93. Doi: 10.3934/mfc.2021044

This issue Previous Article On complex modified Bernstein-Stancu operators Next Article Behavior in $ L^\infty $ of convolution transforms with dilated kernels

On a special class of modified integral operators preserving some exponential functions

Gümrah Uysal

Department of Computer Technologies, Division of Technology of Security of Informatics, Karabuk University, Karabuk, Turkey

Received: August 2021

Revised: December 2021

Early access: January 2022

Published: February 2023

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Abstract

In the present paper, we consider a general class of operators enriched with some properties in order to act on $ C^{\ast }( \mathbb{R} _{0}^{+}) $. We establish uniform convergence of the operators for every function in $ C^{\ast }( \mathbb{R} _{0}^{+}) $ on $ \mathbb{R} _{0}^{+} $. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.

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Mathematics Subject Classification: Primary: 41A35, 41A25; Secondary: 41A36, 47G10.

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Figure 1. $ a = \frac{1}{2} $ and $ n = 5 $

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Figure 2. $ a = \frac{3}{4} $ and $ n = 5 $

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Figure 3. $ a = \frac{3}{10} $ and $ n = 5 $

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Figure 4. $ a = \frac{1}{2} $ and $ n = 5 $

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