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 Lp spaces. In the existing literature, the main assumption in the weight-type results is that the derivative...
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| Published in | Mathematics (Basel) Vol. 10; no. 5; p. 735 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Basel
MDPI AG
01.03.2022
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| Abstract | 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 Lp 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 Lp spaces. Furthermore, we give some new error estimations of the Chebyshev functional and applications to the one-point weight integral formulas. |
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| AbstractList | 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 Lp 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 Lp spaces. Furthermore, we give some new error estimations of the Chebyshev functional and applications to the one-point weight integral formulas. |
| Author | Kovač, Sanja Vukelić, Ana |
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| Cites_doi | 10.1186/1029-242X-2013-1 10.1016/S0898-1221(99)00342-9 10.1016/j.na.2007.01.069 10.1007/978-94-017-1043-5 10.1016/S0898-1221(97)00084-9 10.1007/s41478-019-00177-1 10.1016/S0898-1221(01)00135-3 10.1016/j.camwa.2009.03.089 |
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| Copyright | 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| References | Alomari (ref_8) 2020; 28 (ref_12) 2008; 68 Rehman (ref_5) 2016; 12 ref_2 (ref_4) 2000; 39 Rafiq (ref_7) 2006; 7 (ref_11) 2010; 13 Niezgoda (ref_10) 2009; 58 Hussain (ref_6) 2013; 2013 (ref_1) 1934; 39 Cheng (ref_9) 2001; 42 Dragomir (ref_3) 1997; 39 |
| References_xml | – volume: 7 start-page: 124 year: 2006 ident: ref_7 article-title: A generalized Ostrowski–Grüss-type inequality for twice differentiable mappings and applications publication-title: J. Inequalities Pure Appl. Math. – volume: 2013 start-page: 1 year: 2013 ident: ref_6 article-title: A generalized Ostrowski–Grüss-type inequality for bounded differentiable mappings and its applications publication-title: J. Inequal. Appl. doi: 10.1186/1029-242X-2013-1 – volume: 39 start-page: 161 year: 2000 ident: ref_4 article-title: Improvement and further generalization of inequalities of Ostrowski–Grüss-type publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(99)00342-9 – volume: 13 start-page: 579 year: 2010 ident: ref_11 article-title: Weighted version of general integral formula publication-title: Math. Inequal. Appl. – volume: 68 start-page: 2445 year: 2008 ident: ref_12 article-title: A generalization of general two-point formula with applications in numerical integration publication-title: Nonlinear Anal. Theory Methods Appl. doi: 10.1016/j.na.2007.01.069 – volume: 39 start-page: 215 year: 1934 ident: ref_1 article-title: Uber das maximum des absoluten betrages von 1b−a∫abf(x)dx∫abg(x)dx publication-title: Math. Z. – ident: ref_2 doi: 10.1007/978-94-017-1043-5 – volume: 39 start-page: 15 year: 1997 ident: ref_3 article-title: An inequality of Ostrowski–Grüss’ type and its applications to estimation of error bounds for some special means and for some numerical quadrature rules publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(97)00084-9 – volume: 28 start-page: 623 year: 2020 ident: ref_8 article-title: Two-point Ostrowski and Ostrowski–Grüss-type inequalities with applications publication-title: J. Anal. doi: 10.1007/s41478-019-00177-1 – volume: 42 start-page: 109 year: 2001 ident: ref_9 article-title: Improvement of some Ostrowski–Grüss-type inequalities publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(01)00135-3 – volume: 12 start-page: 180 year: 2016 ident: ref_5 article-title: On Chebyshev Functional and Ostrowski–Grus Type Inequalities for Two Coordinates publication-title: Int. J. Anal. Appl. – volume: 58 start-page: 589 year: 2009 ident: ref_10 article-title: A new inequality of Ostrowski–Grüss-type and applications to some numerical quadrature rules publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2009.03.089 |
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| SubjectTerms | Chebyshev approximation Chebyshev functional Derivatives Functionals Functions (mathematics) Grüss inequality Inequality Mathematical functions Ostrowski inequality weight integral formula |
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| Title | Companion to the Ostrowski–Grüss-Type Inequality of the Chebyshev Functional with an Application |
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