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Journals / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 4 Issue: 2

Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex

Sevda Sezer(AKDENİZ ÜNİVERSİTESİ)0000-0001-6448-193X
Pages
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Publication Date
2021-06-01
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Also, we suggest an upper bound for error in numerical integration of $p$-convex functions via composite trapezoid rule.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values of the first derivatives are $p$-convex.
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Key Findings & Data:By means of the obtained inequalities, some bound functions involving beta functions and hypergeometric functions are derived as applications.
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Conclusion & Impact:Also, we suggest an upper bound for error in numerical integration of $p$-convex functions via composite trapezoid rule.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hermite-Hadamard inequality · $p$-convex function · Convexity

Abstract

In this paper, we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values of the first derivatives are $p$-convex. By means of the obtained inequalities, some bound functions involving beta functions and hypergeometric functions are derived as applications. Also, we suggest an upper bound for error in numerical integration of $p$-convex functions via composite trapezoid rule.

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Cite This Article

Sezer, S. (2021). Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex. Fundamental Journal of Mathematics and Applications, Volume: 4 Issue: 2. https://doi.org/10.33401/fujma.881979

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