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Journals / Constructive Mathematical Analysis / 2026 / Volume: 9 Issue: 1

Several integral inequalities for strongly $(\alpha, m)$-convex functions with modulus

Bo-Yan Xi(Inner Mongolia Minzu University)0000-0003-4528-2331
Tian-Yu Zhang(Inner Mongolia Minzu University)0000-0001-7209-7241
Feng Qi(Retirement)0000-0001-6239-2968
Pages
—
Publication Date
2026-03-06
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⚡ TL;DR(Too Long; Didn't Read)

In the paper, the authors introduce the concept of strongly $(\alpha, m)$-convex function with modulus, establish several new integral identities, and, by virtue of these newly-identities and H\"older's inequality, present some new integral inequalities of the Hermite--Hadamard type for strongly $(\alpha, m)$-convex functions with modulus.

📌 3 Key Takeaways

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Objective & Hypothesis:In the paper, the authors introduce the concept of strongly $(\alpha, m)$-convex function with modulus, establish several new integral identities, and, by virtue of these newly-identities and H\"older's inequality, present some new integral inequalities of the Hermite--Hadamard type for strongly $(\alpha, m)$-convex functions with modulus.
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Key Findings & Data:In the paper, the authors introduce the concept of strongly $(\alpha, m)$-convex function with modulus, establish several new integral identities, and, by virtue of these newly-identities and H\"older's inequality, present some new integral inequalities of the Hermite--Hadamard type for strongly $(\alpha, m)$-convex functions with modulus.
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Conclusion & Impact:In the paper, the authors introduce the concept of strongly $(\alpha, m)$-convex function with modulus, establish several new integral identities, and, by virtue of these newly-identities and H\"older's inequality, present some new integral inequalities of the Hermite--Hadamard type for strongly $(\alpha, m)$-convex functions with modulus.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hermite--Hadamard's inequality · strongly (α · m)-convex function

Abstract

In the paper, the authors introduce the concept of strongly $(\alpha, m)$-convex function with modulus, establish several new integral identities, and, by virtue of these newly-identities and H\"older's inequality, present some new integral inequalities of the Hermite--Hadamard type for strongly $(\alpha, m)$-convex functions with modulus.

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Cite This Article

Xi, B., Zhang, T., Qi, F. (2026). Several integral inequalities for strongly $(\alpha, m)$-convex functions with modulus. Constructive Mathematical Analysis, Volume: 9 Issue: 1. https://doi.org/10.33205/cma.1868426

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