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

Paul Bosch; Jorge A. Paz Moyado; José M. Rodríguez-García; José M. Sigarreta; Paul Bosch; Jorge A. Paz Moyado; José M. Rodríguez-García; José M. Sigarreta

doi:10.3934/math.2025301

AIMS Mathematics

2025, Volume 10, Issue 3: 6574-6588. doi: 10.3934/math.2025301

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Research article

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

1.
Facultad de Ingeniería, Universidad del Desarrollo, Ave. Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago, Chile
2.
Universidad Autónoma de Guerrero, Centro Acapulco, CP 39610, Acapulco de Juárez, Guerrero, México
3.
Universidad Carlos Ⅲ de Madrid, ROR: https://ror.org/03ths8210, Departamento de Matemáticas, Avenida de la Universidad, 30 (edificio Sabatini), 28911 Leganés (Madrid), Spain
4.
Universidad Autónoma de Guerrero, Centro Acapulco, CP 39610, Acapulco de Juárez, Guerrero, México

Received: 26 November 2024 Revised: 29 January 2025 Accepted: 12 February 2025 Published: 25 March 2025
MSC : 26A33, 26A51, 26D15

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.
- Jensen's inequality,
- fractional derivatives and integrals,
- fractional integral inequalities
Citation: Paul Bosch, Jorge A. Paz Moyado, José M. Rodríguez-García, José M. Sigarreta. Refinement of Jensen-type inequalities: fractional extensions (global and local)[J]. AIMS Mathematics, 2025, 10(3): 6574-6588. doi: 10.3934/math.2025301

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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.

References

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