Stancu-Type Generalized <i>q</i>-Bernstein–Kantorovich Operators Involving Bézier Bases
We construct the Stancu-type generalization of <i>q</i>-Bernstein operators involving the idea of Bézier bases depending on the shape parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow>&...
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/2057 |
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| author | Wen-Tao Cheng Md Nasiruzzaman Syed Abdul Mohiuddine |
| author_facet | Wen-Tao Cheng Md Nasiruzzaman Syed Abdul Mohiuddine |
| author_sort | Wen-Tao Cheng |
| collection | DOAJ |
| description | We construct the Stancu-type generalization of <i>q</i>-Bernstein operators involving the idea of Bézier bases depending on the shape parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>1</mn><mo>≤</mo><mi>ζ</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula> and obtain auxiliary lemmas. We discuss the local approximation results in term of a Lipschitz-type function based on two parameters and a Lipschitz-type maximal function, as well as other related results for our newly constructed operators. Moreover, we determine the rate of convergence of our operators by means of Peetre’s <i>K</i>-functional and corresponding modulus of continuity. |
| first_indexed | 2024-03-09T23:08:58Z |
| format | Article |
| id | doaj.art-9631588543f54bf1bffedb53bf43e00a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:08:58Z |
| publishDate | 2022-06-01 |
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| series | Mathematics |
| spelling | doaj.art-9631588543f54bf1bffedb53bf43e00a2023-11-23T17:49:01ZengMDPI AGMathematics2227-73902022-06-011012205710.3390/math10122057Stancu-Type Generalized <i>q</i>-Bernstein–Kantorovich Operators Involving Bézier BasesWen-Tao Cheng0Md Nasiruzzaman1Syed Abdul Mohiuddine2School of Mathematics and Physics, Anqing Normal University, Anqing 246133, ChinaDepartment of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of General Required Courses, Mathematics, Faculty of Applied Studies, King Abdulaziz University, Jeddah 21589, Saudi ArabiaWe construct the Stancu-type generalization of <i>q</i>-Bernstein operators involving the idea of Bézier bases depending on the shape parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>1</mn><mo>≤</mo><mi>ζ</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula> and obtain auxiliary lemmas. We discuss the local approximation results in term of a Lipschitz-type function based on two parameters and a Lipschitz-type maximal function, as well as other related results for our newly constructed operators. Moreover, we determine the rate of convergence of our operators by means of Peetre’s <i>K</i>-functional and corresponding modulus of continuity.https://www.mdpi.com/2227-7390/10/12/2057(ζ,<i>q</i>)-Bernstein operatorsBézier basesuniform convergenceLipschitz-type functionsrate of convergence |
| spellingShingle | Wen-Tao Cheng Md Nasiruzzaman Syed Abdul Mohiuddine Stancu-Type Generalized <i>q</i>-Bernstein–Kantorovich Operators Involving Bézier Bases Mathematics (ζ,<i>q</i>)-Bernstein operators Bézier bases uniform convergence Lipschitz-type functions rate of convergence |
| title | Stancu-Type Generalized <i>q</i>-Bernstein–Kantorovich Operators Involving Bézier Bases |
| title_full | Stancu-Type Generalized <i>q</i>-Bernstein–Kantorovich Operators Involving Bézier Bases |
| title_fullStr | Stancu-Type Generalized <i>q</i>-Bernstein–Kantorovich Operators Involving Bézier Bases |
| title_full_unstemmed | Stancu-Type Generalized <i>q</i>-Bernstein–Kantorovich Operators Involving Bézier Bases |
| title_short | Stancu-Type Generalized <i>q</i>-Bernstein–Kantorovich Operators Involving Bézier Bases |
| title_sort | stancu type generalized i q i bernstein kantorovich operators involving bezier bases |
| topic | (ζ,<i>q</i>)-Bernstein operators Bézier bases uniform convergence Lipschitz-type functions rate of convergence |
| url | https://www.mdpi.com/2227-7390/10/12/2057 |
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