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

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  • 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.

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


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

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

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

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

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