Fractional inequalities of Milne type for twice differentiable m-convex and (α,m)-convex functions

In this study, we employ a special identity for twice differentiable functions that has been used in the literature.By combining this identity with Riemann-Liouville fractional integrals, we derive various fractional Milne-type inequalities for functions whose second derivatives in absolute value are m-convex and (, m)-convex.Furthermore, by applying Hlder's and Young's inequalities to these m-convex and (, m)-convex functions, we obtain several novel results.

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Publication Details

Journal
Electronic Journal of Mathematics
Published
2025-09-26
DOI
https://doi.org/10.47443/ejm.2025.045
Primary Topic
Mathematical Inequalities and Applications
Type
article
Field-Weighted Citation Impact
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article

Fractional inequalities of Milne type for twice differentiable m-convex and (α,m)-convex functions

Sinan Aslan, Ahmet Ocak Akdemi̇r
Electronic Journal of Mathematics
Mathematical Inequalities and Applications
article

Fractional inequalities of Milne type for twice differentiable m-convex and (α,m)-convex functions

Sinan Aslan, Ahmet Ocak Akdemi̇r
article en

Abstract

In this study, we employ a special identity for twice differentiable functions that has been used in the literature.By combining this identity with Riemann-Liouville fractional integrals, we derive various fractional Milne-type inequalities for functions whose second derivatives in absolute value are m-convex and (, m)-convex.Furthermore, by applying Hlder's and Young's inequalities to these m-convex and (, m)-convex functions, we obtain several novel results.

Electronic Journal of MathematicsVol. 10
Openalex Percentile: Top 63%
Mathematical Inequalities and Applications
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Fractional inequalities of Milne type for twice differentiable m-convex and (α,m)-convex functions — Sinan Aslan, Ahmet Ocak Akdemi̇r · Electronic Journal of Mathematics (2025) | TGRS Research Map | TGRS