A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties
The topic of approximation with positive linear operators in contemporary functional analysis and theory of functions has emerged in the last century. One of these operators is Meyer–König and Zeller operators and in this study a generalization of Meyer–König and Zeller type operators based on a fun...
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3275 |
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| author | Qing-Bo Cai Khursheed J. Ansari Fuat Usta |
| author_facet | Qing-Bo Cai Khursheed J. Ansari Fuat Usta |
| author_sort | Qing-Bo Cai |
| collection | DOAJ |
| description | The topic of approximation with positive linear operators in contemporary functional analysis and theory of functions has emerged in the last century. One of these operators is Meyer–König and Zeller operators and in this study a generalization of Meyer–König and Zeller type operators based on a function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula> by using two sequences of functions will be presented. The most significant point is that the newly introduced operator preserves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mi>τ</mi><mo>,</mo><msup><mi>τ</mi><mn>2</mn></msup><mo>}</mo></mrow></semantics></math></inline-formula> instead of classical Korovkin test functions. Then asymptotic type formula, quantitative results, and local approximation properties of the introduced operators are given. Finally a numerical example performed by MATLAB is given to visualize the provided theoretical results. |
| first_indexed | 2024-03-10T03:37:07Z |
| format | Article |
| id | doaj.art-57b2de0d1d614671ae2ba6a3fece7c51 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:37:07Z |
| publishDate | 2021-12-01 |
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| series | Mathematics |
| spelling | doaj.art-57b2de0d1d614671ae2ba6a3fece7c512023-11-23T09:26:47ZengMDPI AGMathematics2227-73902021-12-01924327510.3390/math9243275A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation PropertiesQing-Bo Cai0Khursheed J. Ansari1Fuat Usta2School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, ChinaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, Faculty of Arts and Sciences, Düzce University, Düzce 81620, TurkeyThe topic of approximation with positive linear operators in contemporary functional analysis and theory of functions has emerged in the last century. One of these operators is Meyer–König and Zeller operators and in this study a generalization of Meyer–König and Zeller type operators based on a function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula> by using two sequences of functions will be presented. The most significant point is that the newly introduced operator preserves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mi>τ</mi><mo>,</mo><msup><mi>τ</mi><mn>2</mn></msup><mo>}</mo></mrow></semantics></math></inline-formula> instead of classical Korovkin test functions. Then asymptotic type formula, quantitative results, and local approximation properties of the introduced operators are given. Finally a numerical example performed by MATLAB is given to visualize the provided theoretical results.https://www.mdpi.com/2227-7390/9/24/3275Meyer–König and Zeller operatorsmodulus of continuityshape preserving approximationVoronovskaya theoremKorovkin type theorem |
| spellingShingle | Qing-Bo Cai Khursheed J. Ansari Fuat Usta A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties Mathematics Meyer–König and Zeller operators modulus of continuity shape preserving approximation Voronovskaya theorem Korovkin type theorem |
| title | A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties |
| title_full | A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties |
| title_fullStr | A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties |
| title_full_unstemmed | A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties |
| title_short | A Note on New Construction of Meyer-König and Zeller Operators and Its Approximation Properties |
| title_sort | note on new construction of meyer konig and zeller operators and its approximation properties |
| topic | Meyer–König and Zeller operators modulus of continuity shape preserving approximation Voronovskaya theorem Korovkin type theorem |
| url | https://www.mdpi.com/2227-7390/9/24/3275 |
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