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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/11/2018 |
| _version_ | 1797508354977824768 |
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| author | Ana Maria Acu Gancho Tachev |
| author_facet | Ana Maria Acu Gancho Tachev |
| author_sort | Ana Maria Acu |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:00:57Z |
| format | Article |
| id | doaj.art-37642d2e5d1941df856ee397466ddd72 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T05:00:57Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-37642d2e5d1941df856ee397466ddd722023-11-23T01:43:29ZengMDPI AGSymmetry2073-89942021-10-011311201810.3390/sym13112018Yet Another New Variant of Szász–Mirakyan OperatorAna Maria Acu0Gancho Tachev1Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5–7, 550012 Sibiu, RomaniaDepartment of Mathematics, University of Architecture Civil Engineering and Geodesy, 1046 Sofia, BulgariaIn 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.https://www.mdpi.com/2073-8994/13/11/2018Szász–Mirakyan operatorsweighted approximationuniform convergenceexponential functions |
| spellingShingle | Ana Maria Acu Gancho Tachev Yet Another New Variant of Szász–Mirakyan Operator Symmetry Szász–Mirakyan operators weighted approximation uniform convergence exponential functions |
| title | 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_short | Yet Another New Variant of Szász–Mirakyan Operator |
| title_sort | yet another new variant of szasz mirakyan operator |
| topic | Szász–Mirakyan operators weighted approximation uniform convergence exponential functions |
| url | https://www.mdpi.com/2073-8994/13/11/2018 |
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