Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application
Recently, there have been many proven results of the Ostrowski–Grüss-type inequality regarding the error bounds for the Chebyshev functional when the functions or their derivatives belong to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/5/735 |
| _version_ | 1797474517383118848 |
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| author | Sanja Kovač Ana Vukelić |
| author_facet | Sanja Kovač Ana Vukelić |
| author_sort | Sanja Kovač |
| collection | DOAJ |
| description | Recently, there have been many proven results of the Ostrowski–Grüss-type inequality regarding the error bounds for the Chebyshev functional when the functions or their derivatives belong to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> spaces. In the existing literature, the main assumption in the weight-type results is that the derivative of the function is bounded by two constant functions. The aim of our paper is to extend those results in a way that the derivative of the function is bounded by two functions in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> spaces. Furthermore, we give some new error estimations of the Chebyshev functional and applications to the one-point weight integral formulas. |
| first_indexed | 2024-03-09T20:31:14Z |
| format | Article |
| id | doaj.art-936ae71b63cb4f63b5217d55404aff3a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T20:31:14Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-936ae71b63cb4f63b5217d55404aff3a2023-11-23T23:22:51ZengMDPI AGMathematics2227-73902022-02-0110573510.3390/math10050735Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an ApplicationSanja Kovač0Ana Vukelić1Faculty of Geotechnical Engineering, University of Zagreb, 42000 Varaždin, CroatiaFaculty of Food and Biotechnology, University of Zagreb, 10000 Zagreb, CroatiaRecently, there have been many proven results of the Ostrowski–Grüss-type inequality regarding the error bounds for the Chebyshev functional when the functions or their derivatives belong to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> spaces. In the existing literature, the main assumption in the weight-type results is that the derivative of the function is bounded by two constant functions. The aim of our paper is to extend those results in a way that the derivative of the function is bounded by two functions in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> spaces. Furthermore, we give some new error estimations of the Chebyshev functional and applications to the one-point weight integral formulas.https://www.mdpi.com/2227-7390/10/5/735Chebyshev functionalGrüss inequalityOstrowski inequalityweight integral formula |
| spellingShingle | Sanja Kovač Ana Vukelić Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application Mathematics Chebyshev functional Grüss inequality Ostrowski inequality weight integral formula |
| title | Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application |
| title_full | Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application |
| title_fullStr | Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application |
| title_full_unstemmed | Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application |
| title_short | Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application |
| title_sort | companion to the ostrowski gruss type inequality of the chebyshev functional with an application |
| topic | Chebyshev functional Grüss inequality Ostrowski inequality weight integral formula |
| url | https://www.mdpi.com/2227-7390/10/5/735 |
| work_keys_str_mv | AT sanjakovac companiontotheostrowskigrusstypeinequalityofthechebyshevfunctionalwithanapplication AT anavukelic companiontotheostrowskigrusstypeinequalityofthechebyshevfunctionalwithanapplication |