Some new Jensen–Mercer type integral inequalities are established via fractional operators

In this study, we present new variants of the Hermite–Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the cla...

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Autores principales: Bayraktar, Bahtiyar, Kórus, Péter, Nápoles Valdés, Juan Eduardo
Formato: Artículo
Lenguaje:Inglés
Publicado: MDPI AG 2026
Materias:
Convex functions
(h, m)-convex functions
Jensen–Mercer inequality
Hermite–Hadamard inequality
Hölder inequality
Power mean inequality
Non-conformable fractional operators
Acceso en línea:http://repositorio.unne.edu.ar/handle/123456789/60058
Aporte de:
RIUNNE - Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE) de Universidad Nacional del Nordeste
id I48-R184-123456789-60058
record_format dspace
spelling I48-R184-123456789-600582026-02-14T20:20:51Z Some new Jensen–Mercer type integral inequalities are established via fractional operators Bayraktar, Bahtiyar Kórus, Péter Nápoles Valdés, Juan Eduardo Convex functions (h, m)-convex functions Jensen–Mercer inequality Hermite–Hadamard inequality Hölder inequality Power mean inequality Non-conformable fractional operators In this study, we present new variants of the Hermite–Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the classical Jensen–Mercer inequality and its variants for (ℎ, ) -convex modified functions proven in this paper. In addition to showing that our results support previously known results from the literature, we provide examples of their application. 2026-02-13T18:23:32Z 2026-02-13T18:23:32Z 2023 Artículo Bayraktar, Bahtiyar, Kórus, Péter y Nápoles Valdés, Juan Eduardo, 2023. Some new Jensen–Mercer type integral inequalities are established via fractional operators. Axioms. Basel: MDPI AG, vol. 12, no. 6, p. 1-17. ISSN 2075-1680. 2075-1680 http://repositorio.unne.edu.ar/handle/123456789/60058 eng https://doi.org/10.3390/axioms12060517 openAccess http://creativecommons.org/licenses/by/2.5/ar/ application/pdf p. 1-17 application/pdf MDPI AG Axioms, 2023, vol. 12, no. 6, p. 1-17.
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 functions
(h, m)-convex functions
Jensen–Mercer inequality
Hermite–Hadamard inequality
Hölder inequality
Power mean inequality
Non-conformable fractional operators
spellingShingle Convex functions
(h, m)-convex functions
Jensen–Mercer inequality
Hermite–Hadamard inequality
Hölder inequality
Power mean inequality
Non-conformable fractional operators
Bayraktar, Bahtiyar
Kórus, Péter
Nápoles Valdés, Juan Eduardo
Some new Jensen–Mercer type integral inequalities are established via fractional operators
topic_facet Convex functions
(h, m)-convex functions
Jensen–Mercer inequality
Hermite–Hadamard inequality
Hölder inequality
Power mean inequality
Non-conformable fractional operators
description In this study, we present new variants of the Hermite–Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the classical Jensen–Mercer inequality and its variants for (ℎ, ) -convex modified functions proven in this paper. In addition to showing that our results support previously known results from the literature, we provide examples of their application.
format Artículo
author Bayraktar, Bahtiyar
Kórus, Péter
Nápoles Valdés, Juan Eduardo
author_facet Bayraktar, Bahtiyar
Kórus, Péter
Nápoles Valdés, Juan Eduardo
author_sort Bayraktar, Bahtiyar
title Some new Jensen–Mercer type integral inequalities are established via fractional operators
title_short Some new Jensen–Mercer type integral inequalities are established via fractional operators
title_full Some new Jensen–Mercer type integral inequalities are established via fractional operators
title_fullStr Some new Jensen–Mercer type integral inequalities are established via fractional operators
title_full_unstemmed Some new Jensen–Mercer type integral inequalities are established via fractional operators
title_sort some new jensen–mercer type integral inequalities are established via fractional operators
publisher MDPI AG
publishDate 2026
url http://repositorio.unne.edu.ar/handle/123456789/60058
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AT koruspeter somenewjensenmercertypeintegralinequalitiesareestablishedviafractionaloperators
AT napolesvaldesjuaneduardo somenewjensenmercertypeintegralinequalitiesareestablishedviafractionaloperators
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