Volume 34, Issue 4
Approximation by a Complex Post-Widder Type Operator

Anal. Theory Appl., 34 (2018), pp. 297-305.

Published online: 2018-11

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• Abstract

In the present article, we deal with the so-called overconvergence phenomenon in $\mathbb{C}$ of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane. In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.

• Keywords

Real and complex Post-Widder type operator, overconvergence phenomenon, approximation estimate, Voronovskaya-type result, exact error estimation.

41A25, 41A30, 30E10

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• TXT
@Article{ATA-34-297, author = {}, title = {Approximation by a Complex Post-Widder Type Operator}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {4}, pages = {297--305}, abstract = {

In the present article, we deal with the so-called overconvergence phenomenon in $\mathbb{C}$ of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane. In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2018-0003}, url = {http://global-sci.org/intro/article_detail/ata/12843.html} }
TY - JOUR T1 - Approximation by a Complex Post-Widder Type Operator JO - Analysis in Theory and Applications VL - 4 SP - 297 EP - 305 PY - 2018 DA - 2018/11 SN - 34 DO - http://doi.org/10.4208/ata.OA-2018-0003 UR - https://global-sci.org/intro/article_detail/ata/12843.html KW - Real and complex Post-Widder type operator, overconvergence phenomenon, approximation estimate, Voronovskaya-type result, exact error estimation. AB -

In the present article, we deal with the so-called overconvergence phenomenon in $\mathbb{C}$ of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane. In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.

Sorin G. Gal & Vijay Gupta. (1970). Approximation by a Complex Post-Widder Type Operator. Analysis in Theory and Applications. 34 (4). 297-305. doi:10.4208/ata.OA-2018-0003
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