Some new estimates of integral inequalities and their applications

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 kno...

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Autores principales: Bayraktar, Bahtiyar, Butt, Saad Ihsan, Nápoles Valdés, Juan Eduardo, Rabossi, Florencia
Formato: Artículo
Lenguaje:Inglés
Publicado: National Academy of Sciences of Ukraine. Institute of Mathematics 2026
Materias:
Convex function
Quasi-convex
Hermite-Hadamard type inequality
Simpson type inequalities
Riemann-Liouville fraction integrals
Lipschitz condition
Lagrange theorem
Acceso en línea:http://repositorio.unne.edu.ar/handle/123456789/60050
Aporte de:
RIUNNE - Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE) de Universidad Nacional del Nordeste
id I48-R184-123456789-60050
record_format dspace
spelling I48-R184-123456789-600502026-02-13T10:02:38Z Some new estimates of integral inequalities and their applications Деякі нові оцінки інтегральних нерівностей та їх застосування Bayraktar, Bahtiyar Butt, Saad Ihsan Nápoles Valdés, Juan Eduardo Rabossi, Florencia Convex function Quasi-convex Hermite-Hadamard type inequality Simpson type inequalities Riemann-Liouville fraction integrals Lipschitz condition Lagrange theorem 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. Отримано кiлька нових iнтегральних нерiвностей у термiнах дробових iнтегральних операторiв для функцiй, першi похiднi яких задовольняють умови теореми Лагранжа або умову Лiпшиця. У деяких частинних випадках отриманi результати дають кращi верхнi оцiнки, нiж вiдомi в лiтературi для нерiвностi типу Буллена та правосторонньої нерiвностi типу Адамара. Насамкiнець обговорено деякi оцiнки похибки для формули трапецiї. 2026-02-12T20:13:06Z 2026-02-12T20:13:06Z 2024 Artículo Bayraktar, Bahtiyar, et al., 2024. Some new estimates of integral inequalities and their applications. Ukrainian Mathematical Journal. Kyiv: National Academy of Sciences of Ukraine. Institute of Mathematics, vol. 76, no. 2, p. 159-178. ISSN 1027-3190. 1027-3190 http://repositorio.unne.edu.ar/handle/123456789/60050 eng https://doi.org/10.3842/umzh.v76i2.7266 closedAccess http://creativecommons.org/licenses/by-nc-nd/2.5/ar/ application/pdf p. 159-178 application/pdf National Academy of Sciences of Ukraine. Institute of Mathematics Ukrainian Mathematical Journal, 2024, vol. 76, no. 2, p. 159-178.
institution Universidad Nacional del Nordeste
institution_str I-48
repository_str R-184
collection RIUNNE - Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)
language Inglés
topic Convex function
Quasi-convex
Hermite-Hadamard type inequality
Simpson type inequalities
Riemann-Liouville fraction integrals
Lipschitz condition
Lagrange theorem
spellingShingle Convex function
Quasi-convex
Hermite-Hadamard type inequality
Simpson type inequalities
Riemann-Liouville fraction integrals
Lipschitz condition
Lagrange theorem
Bayraktar, Bahtiyar
Butt, Saad Ihsan
Nápoles Valdés, Juan Eduardo
Rabossi, Florencia
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
description 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.
format Artículo
author Bayraktar, Bahtiyar
Butt, Saad Ihsan
Nápoles Valdés, Juan Eduardo
Rabossi, Florencia
author_facet Bayraktar, Bahtiyar
Butt, Saad Ihsan
Nápoles Valdés, Juan Eduardo
Rabossi, Florencia
author_sort Bayraktar, Bahtiyar
title Some new estimates of integral inequalities and their applications
title_short 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_sort some new estimates of integral inequalities and their applications
publisher National Academy of Sciences of Ukraine. Institute of Mathematics
publishDate 2026
url http://repositorio.unne.edu.ar/handle/123456789/60050
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