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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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/37642d2e5d1941df856ee397466ddd72 |
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| Sumario: | 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. |
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