Hermite-Hadamard Inequalities via Riemann-Liouville Fractional Integrals with Generalized Convex Functions

Muhammad Samraiz; Tahira Atta; Saima Naheed; Gauhar Rahman; Miguel Vivas-Cortez

doi:10.29020/nybg.ejpam.v18i3.6413

Hermite-Hadamard Inequalities via Riemann-Liouville Fractional Integrals with Generalized Convex Functions

Muhammad Samraiz
, Tahira Atta
, Saima Naheed
, Gauhar Rahman
, Miguel Vivas-Cortez

Research output: Contribution to journal › Article › peer-review

Abstract

In this study, novel fractional integral inequalities for twice-differentiable geometrically arithmetically (α, m)-convex functions are presented. The classical Riemann-Liouville fractional integrals are used to obtain several new identities. By employing the above convexity, Hermite-Hadamard type inequalities are investigated using these identities. The main findings of this work extend the existing literature and are derived as special cases.

Original language	English
Article number	6413
Journal	European Journal of Pure and Applied Mathematics
Volume	18
Issue number	3
DOIs	https://doi.org/10.29020/nybg.ejpam.v18i3.6413
State	Published - Jul 2025

Keywords

Fractional Integrals
Geometrically Arithmetically (α
Hermite-Hadamard Type Inequalities
Hölder’s Inequality
m)-Convex

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10.29020/nybg.ejpam.v18i3.6413

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title = "Hermite-Hadamard Inequalities via Riemann-Liouville Fractional Integrals with Generalized Convex Functions",

abstract = "In this study, novel fractional integral inequalities for twice-differentiable geometrically arithmetically (α, m)-convex functions are presented. The classical Riemann-Liouville fractional integrals are used to obtain several new identities. By employing the above convexity, Hermite-Hadamard type inequalities are investigated using these identities. The main findings of this work extend the existing literature and are derived as special cases.",

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author = "Muhammad Samraiz and Tahira Atta and Saima Naheed and Gauhar Rahman and Miguel Vivas-Cortez",

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T1 - Hermite-Hadamard Inequalities via Riemann-Liouville Fractional Integrals with Generalized Convex Functions

AU - Samraiz, Muhammad

AU - Atta, Tahira

AU - Naheed, Saima

AU - Rahman, Gauhar

AU - Vivas-Cortez, Miguel

PY - 2025/7

Y1 - 2025/7

N2 - In this study, novel fractional integral inequalities for twice-differentiable geometrically arithmetically (α, m)-convex functions are presented. The classical Riemann-Liouville fractional integrals are used to obtain several new identities. By employing the above convexity, Hermite-Hadamard type inequalities are investigated using these identities. The main findings of this work extend the existing literature and are derived as special cases.

AB - In this study, novel fractional integral inequalities for twice-differentiable geometrically arithmetically (α, m)-convex functions are presented. The classical Riemann-Liouville fractional integrals are used to obtain several new identities. By employing the above convexity, Hermite-Hadamard type inequalities are investigated using these identities. The main findings of this work extend the existing literature and are derived as special cases.

KW - Fractional Integrals

KW - Geometrically Arithmetically (α

KW - Hermite-Hadamard Type Inequalities

KW - Hölder’s Inequality

KW - m)-Convex

UR - https://www.scopus.com/pages/publications/105013635685

U2 - 10.29020/nybg.ejpam.v18i3.6413

DO - 10.29020/nybg.ejpam.v18i3.6413

M3 - Artículo

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SN - 1307-5543

VL - 18

JO - European Journal of Pure and Applied Mathematics

JF - European Journal of Pure and Applied Mathematics

IS - 3

M1 - 6413

ER -

Hermite-Hadamard Inequalities via Riemann-Liouville Fractional Integrals with Generalized Convex Functions

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Keywords

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