On One- and Two-Dimensional <i>α</i>–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties
The goal of this research article is to introduce a sequence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>–Stancu–Schurer–Kantorovich o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3227 |
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| author | Md. Heshamuddin Nadeem Rao Bishnu P. Lamichhane Adem Kiliçman Mohammad Ayman-Mursaleen |
| author_facet | Md. Heshamuddin Nadeem Rao Bishnu P. Lamichhane Adem Kiliçman Mohammad Ayman-Mursaleen |
| author_sort | Md. Heshamuddin |
| collection | DOAJ |
| description | The goal of this research article is to introduce a sequence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>–Stancu–Schurer–Kantorovich operators. We calculate moments and central moments and find the order of approximation with the aid of modulus of continuity. A Voronovskaja-type approximation result is also proven. Next, error analysis and convergence of the operators for certain functions are presented numerically and graphically. Furthermore, two-dimensional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>–Stancu–Schurer–Kantorovich operators are constructed and their rate of convergence, graphical representation of approximation and numerical error estimates are presented. |
| first_indexed | 2024-03-09T23:16:57Z |
| format | Article |
| id | doaj.art-c5aefa0b7fb747fe950ce46cc187933d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:16:57Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c5aefa0b7fb747fe950ce46cc187933d2023-11-23T17:34:54ZengMDPI AGMathematics2227-73902022-09-011018322710.3390/math10183227On One- and Two-Dimensional <i>α</i>–Stancu–Schurer–Kantorovich Operators and Their Approximation PropertiesMd. Heshamuddin0Nadeem Rao1Bishnu P. Lamichhane2Adem Kiliçman3Mohammad Ayman-Mursaleen4Department of Natural & Applied Sciences, Glocal University, Saharanpur-247121, Uttar Pradesh, IndiaDepartment of Applied Sciences & Humanities, Panipat Institute of Engineering and Technology, Pattikalyana, Samalkha, Panipat-132102, Haryana, IndiaSchool of Information & Physical Sciences, The University of Newcastle, University Drive, Callaghan, NSW 2308, AustraliaDepartment of Mathematics & Statistics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, MalaysiaSchool of Information & Physical Sciences, The University of Newcastle, University Drive, Callaghan, NSW 2308, AustraliaThe goal of this research article is to introduce a sequence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>–Stancu–Schurer–Kantorovich operators. We calculate moments and central moments and find the order of approximation with the aid of modulus of continuity. A Voronovskaja-type approximation result is also proven. Next, error analysis and convergence of the operators for certain functions are presented numerically and graphically. Furthermore, two-dimensional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>–Stancu–Schurer–Kantorovich operators are constructed and their rate of convergence, graphical representation of approximation and numerical error estimates are presented.https://www.mdpi.com/2227-7390/10/18/3227rate of convergenceorder of approximationmodulus of continuityweighted approximationA-statistical approximation |
| spellingShingle | Md. Heshamuddin Nadeem Rao Bishnu P. Lamichhane Adem Kiliçman Mohammad Ayman-Mursaleen On One- and Two-Dimensional <i>α</i>–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties Mathematics rate of convergence order of approximation modulus of continuity weighted approximation A-statistical approximation |
| title | On One- and Two-Dimensional <i>α</i>–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties |
| title_full | On One- and Two-Dimensional <i>α</i>–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties |
| title_fullStr | On One- and Two-Dimensional <i>α</i>–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties |
| title_full_unstemmed | On One- and Two-Dimensional <i>α</i>–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties |
| title_short | On One- and Two-Dimensional <i>α</i>–Stancu–Schurer–Kantorovich Operators and Their Approximation Properties |
| title_sort | on one and two dimensional i α i stancu schurer kantorovich operators and their approximation properties |
| topic | rate of convergence order of approximation modulus of continuity weighted approximation A-statistical approximation |
| url | https://www.mdpi.com/2227-7390/10/18/3227 |
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