Szász–Beta Operators Linking Frobenius–Euler–Simsek-Type Polynomials
This manuscript associates with a study of Frobenius–Euler–Simsek-type Polynomials. In this research work, we construct a new sequence of Szász–Beta type operators via Frobenius–Euler–Simsek-type Polynomials to discuss approximation properties for the Lebesgue integrable functions, i.e., <inline-...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/6/418 |
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| Summary: | This manuscript associates with a study of Frobenius–Euler–Simsek-type Polynomials. In this research work, we construct a new sequence of Szász–Beta type operators via Frobenius–Euler–Simsek-type Polynomials to discuss approximation properties for the Lebesgue integrable functions, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>L</mi><mi>p</mi></msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. Furthermore, estimates in view of test functions and central moments are studied. Next, rate of convergence is discussed with the aid of the Korovkin theorem and the Voronovskaja type theorem. Moreover, direct approximation results in terms of modulus of continuity of first- and second-order, Peetre’s K-functional, Lipschitz type space, and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>r</mi><mrow><mi>t</mi><mi>h</mi></mrow></msup></semantics></math></inline-formula>-order Lipschitz type maximal functions are investigated. In the subsequent section, we present weighted approximation results, and statistical approximation theorems are discussed. To demonstrate the effectiveness and applicability of the proposed operators, we present several illustrative examples and visualize the results graphically. |
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| ISSN: | 2075-1680 |