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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 2

The Hermite-Hadamard type inequalities for the functions whose derivative is logarithmic $p$-convex function

Gültekin Tınaztepe(AKDENIZ UNIVERSITY)0000-0001-7594-1620
Sinem Sezer Evcan(AKDENIZ UNIVERSITY)0000-0003-2066-7833
Zeynep Eken(AKDENIZ UNIVERSITY)0000-0002-8939-4653
Sevda Sezer(AKDENIZ UNIVERSITY)0000-0001-6448-193X
Pages
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Publication Date
2025-04-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Through the obtained results, a bound for numerical integration of such type functions is provided.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:By means of an integral identity, several Hermite-Hadamard type inequalities are presented in this study for a function whose derivative's absolute value is the log-p-convex function.
📊
Key Findings & Data:With the use of these findings, we are able to determine the boundaries in terms of elementary functions for certain specific functions, such as the imaginary error function, the exponential integral, the hyperbolic sine and cosine functions.
💡
Conclusion & Impact:Through the obtained results, a bound for numerical integration of such type functions is provided.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:p-convex set · log p-convex function · p-convex function

Abstract

By means of an integral identity, several Hermite-Hadamard type inequalities are presented in this study for a function whose derivative's absolute value is the log-p-convex function. With the use of these findings, we are able to determine the boundaries in terms of elementary functions for certain specific functions, such as the imaginary error function, the exponential integral, the hyperbolic sine and cosine functions. Additionally, a relationship between beta function, the hyperbolic sine and cosine functions is stated. Through the obtained results, a bound for numerical integration of such type functions is provided.

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Cite This Article

Tınaztepe, G., Evcan, S. S., Eken, Z., Sezer, S. (2025). The Hermite-Hadamard type inequalities for the functions whose derivative is logarithmic $p$-convex function. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 2. https://doi.org/10.15672/hujms.1444589

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