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Research Article | Open Access

Refinement of Jensen-type inequalities: fractional extensions (global and local)

Paul Bosch1, Jorge A. Paz Moyado2, José M. Rodríguez-García3, José M. Sigarreta4( )
Facultad de Ingeniería, Universidad del Desarrollo, Ave. Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago, Chile
Universidad Autónoma de Guerrero, Centro Acapulco, CP 39610, Acapulco de Juárez, Guerrero, México
Universidad Carlos Ⅲ de Madrid, ROR: https://ror.org/03ths8210, Departamento de Matemáticas, Avenida de la Universidad, 30 (edificio Sabatini), 28911 Leganés (Madrid), Spain
Universidad Autónoma de Guerrero, Centro Acapulco, CP 39610, Acapulco de Juárez, Guerrero, México
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Abstract

In this paper, our main objective was to establish new refinements of Jensen's inequality. We focused on the class of convex and harmonic convex functions. In addition, we extended these results to the generalized Caputo-type fractional integral and the generalized local fractional derivative.

Keywords

Jensen's inequalityfractional derivatives and integralsfractional integral inequalities
CLC number: 26A33, 26A51, 26D15

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 6574-6588
DOI: 10.3934/math.2025301

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Bosch P, Moyado JAP, Rodríguez-García JM, et al. Refinement of Jensen-type inequalities: fractional extensions (global and local). AIMS Mathematics, 2025, 10(3): 6574-6588. https://doi.org/10.3934/math.2025301

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Received: 26 November 2024
Revised: 29 January 2025
Accepted: 12 February 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)