Some new estimates of integral inequalities and their applications
UDC 517.9, 517.928 We obtain several new integral inequalities in terms of fractional integral  operators for the functions whose first derivatives satisfy either the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, the results obtained...
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| author | Bayraktar, B. Butt, S. I. Nápoles, J. E. Rabossi, F. Bayraktar, B. Butt, S. I. Nápoles, J. E. Rabossi, F. |
| author_facet | Bayraktar, B. Butt, S. I. Nápoles, J. E. Rabossi, F. Bayraktar, B. Butt, S. I. Nápoles, J. E. Rabossi, F. |
| author_sort | Bayraktar, B. |
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| datestamp_date | 2024-06-19T00:35:11Z |
| description | UDC 517.9, 517.928
We obtain several new integral inequalities in terms of fractional integral  operators for the functions whose first derivatives satisfy either the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, the results obtained provide better upper estimates than those known in the literature for Bullen-type inequality and Hadamard-type right-hand side inequality. Finally, some error estimates for the trapezoidal formula are discussed. |
| doi_str_mv | 10.3842/umzh.v76i2.7266 |
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Ukrainian Mathematical Journal
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Some New Estimates for Integral Inequalities and Their Applications
Published: 16 August 2024
Volume 76, pages 169–191, (2024)
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B. Bayraktar1,
S. I. Butt2,
J. E. Nápoles3,4 &
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F. Rabossi4
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We obtain several new integral inequalities in terms of fractional integral operators for the functions whose first derivatives satisfy either the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, the obtained results provide better upper estimates than the results known in the literature for the Bullen-type inequality and the Hadamard-type right-hand side inequality. Finally, some error estimates for the trapezoidal formula are discussed.
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Authors and Affiliations
Faculty of Education, Bursa Uludag University, Gorukle Campus, Bursa, Turkey
B. Bayraktar
COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
S. I. Butt
UNNE, FaCENA, Corrientes, Argentina
J. E. Nápoles
UTN-FRRE, Resistencia, Chaco, Argentina
J. E. Nápoles & F. Rabossi
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, No. 2, pp. 159–178, February, 2024. Ukrainian DOI: https://doi.org/10.3842/umzh.v76i2.7266.
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Bayraktar, B., Butt, S.I., Nápoles, J.E. et al. Some New Estimates for Integral Inequalities and Their Applications.
Ukr Math J 76, 169–191 (2024). https://doi.org/10.1007/s11253-024-02315-w
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Received: 20 July 2022
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DOI: https://doi.org/10.1007/s11253-024-02315-w
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| institution | Ukrains’kyi Matematychnyi Zhurnal |
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| language | English |
| last_indexed | 2026-03-24T03:32:07Z |
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| spelling | umjimathkievua-article-72662024-06-19T00:35:11Z Some new estimates of integral inequalities and their applications Some new estimates of integral inequalities and their applications Bayraktar, B. Butt, S. I. Nápoles, J. E. Rabossi, F. Bayraktar, B. Butt, S. I. Nápoles, J. E. Rabossi, F. convex function quasi-convex Hermite-Hadamard type inequality Simpson type inequalities Riemann-Liouville fraction integrals Lipschitz condition Lagrange theorem 26A33, 26A51, 26D15 UDC 517.9, 517.928 We obtain several new integral inequalities in terms of fractional integral  operators for the functions whose first derivatives satisfy either the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, the results obtained provide better upper estimates than those known in the literature for Bullen-type inequality and Hadamard-type right-hand side inequality. Finally, some error estimates for the trapezoidal formula are discussed. УДК 517.9, 517.928 Деякі нові оцінки інтегральних нерівностей та їх застосування Отримано кілька нових інтегральних нерівностей у термінах дробових інтегральних операторів для функцій, перші похідні яких задовольняють умови теореми Лагранжа або умову Ліпшиця. У деяких частинних випадках отримані результати дають кращі верхні оцінки, ніж відомі в літературі для нерівності типу Буллена та правосторонньої нерівності типу Адамара. Насамкінець обговорено деякі оцінки похибки  для формули трапеції. Institute of Mathematics, NAS of Ukraine 2024-02-28 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7266 10.3842/umzh.v76i2.7266 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 2 (2024); 159-178 Український математичний журнал; Том 76 № 2 (2024); 159-178 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7266/9723 Copyright (c) 2024 Bahtiyar Bayraktar, Saad Ihsan Butt, Juan Eduardo Napoles, Florencia Rabossi |
| spellingShingle | Bayraktar, B. Butt, S. I. Nápoles, J. E. Rabossi, F. Bayraktar, B. Butt, S. I. Nápoles, J. E. Rabossi, F. Some new estimates of integral inequalities and their applications |
| title | Some new estimates of integral inequalities and their applications |
| title_alt | Some new estimates of integral inequalities and their applications |
| title_full | Some new estimates of integral inequalities and their applications |
| title_fullStr | Some new estimates of integral inequalities and their applications |
| title_full_unstemmed | Some new estimates of integral inequalities and their applications |
| title_short | Some new estimates of integral inequalities and their applications |
| title_sort | some new estimates of integral inequalities and their applications |
| topic_facet | convex function quasi-convex Hermite-Hadamard type inequality Simpson type inequalities Riemann-Liouville fraction integrals Lipschitz condition Lagrange theorem 26A33 26A51 26D15 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7266 |
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