Yet Another New Variant of Szász–Mirakyan Operator

In this paper, we construct a new variant of the classical Szász–Mirakyan operators, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>n</mi></msub></semantics&...

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Auteurs principaux:	Ana Maria Acu, Gancho Tachev
Format:	article
Langue:	EN
Publié:	MDPI AG 2021
Sujets:	Szász–Mirakyan operators weighted approximation uniform convergence exponential functions Mathematics QA1-939
Accès en ligne:	https://doaj.org/article/37642d2e5d1941df856ee397466ddd72
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spelling	oai:doaj.org-article:37642d2e5d1941df856ee397466ddd722021-11-25T19:06:05ZYet Another New Variant of Szász–Mirakyan Operator10.3390/sym131120182073-8994https://doaj.org/article/37642d2e5d1941df856ee397466ddd722021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2018https://doaj.org/toc/2073-8994In this paper, we construct a new variant of the classical Szász–Mirakyan operators, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>n</mi></msub></semantics></math></inline-formula>, which fixes the functions 1 and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>e</mi><mrow><mi>a</mi><mi>x</mi></mrow></msup><mo>,</mo><mspace width="0.166667em"></mspace><mi>x</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mspace width="0.166667em"></mspace><mspace width="0.166667em"></mspace><mi>a</mi><mo>∈</mo><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>. For these operators, we provide a quantitative Voronovskaya-type result. The uniform weighted convergence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>n</mi></msub></semantics></math></inline-formula> and a direct quantitative estimate are obtained. The symmetry of the properties of the classical Szász–Mirakyan operator and of the properties of the new sequence is investigated. Our results improve and extend similar ones on this topic, established in the last decade by many authors.Ana Maria AcuGancho TachevMDPI AGarticleSzász–Mirakyan operatorsweighted approximationuniform convergenceexponential functionsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2018, p 2018 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Szász–Mirakyan operators weighted approximation uniform convergence exponential functions Mathematics QA1-939
spellingShingle	Szász–Mirakyan operators weighted approximation uniform convergence exponential functions Mathematics QA1-939 Ana Maria Acu Gancho Tachev Yet Another New Variant of Szász–Mirakyan Operator
description	In this paper, we construct a new variant of the classical Szász–Mirakyan operators, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>n</mi></msub></semantics></math></inline-formula>, which fixes the functions 1 and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>e</mi><mrow><mi>a</mi><mi>x</mi></mrow></msup><mo>,</mo><mspace width="0.166667em"></mspace><mi>x</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mspace width="0.166667em"></mspace><mspace width="0.166667em"></mspace><mi>a</mi><mo>∈</mo><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>. For these operators, we provide a quantitative Voronovskaya-type result. The uniform weighted convergence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>M</mi><mi>n</mi></msub></semantics></math></inline-formula> and a direct quantitative estimate are obtained. The symmetry of the properties of the classical Szász–Mirakyan operator and of the properties of the new sequence is investigated. Our results improve and extend similar ones on this topic, established in the last decade by many authors.
format	article
author	Ana Maria Acu Gancho Tachev
author_facet	Ana Maria Acu Gancho Tachev
author_sort	Ana Maria Acu
title	Yet Another New Variant of Szász–Mirakyan Operator
title_short	Yet Another New Variant of Szász–Mirakyan Operator
title_full	Yet Another New Variant of Szász–Mirakyan Operator
title_fullStr	Yet Another New Variant of Szász–Mirakyan Operator
title_full_unstemmed	Yet Another New Variant of Szász–Mirakyan Operator
title_sort	yet another new variant of szász–mirakyan operator
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/37642d2e5d1941df856ee397466ddd72
work_keys_str_mv	AT anamariaacu yetanothernewvariantofszaszmirakyanoperator AT ganchotachev yetanothernewvariantofszaszmirakyanoperator
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Yet Another New Variant of Szász–Mirakyan Operator

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