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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
The results provided new inequalities for the class of classical convex functions and the class of harmonic convex functions.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, new lemmas on $p-$convex and $s-p-$convex functions were derived utilizing the integral $\int_{j}^{k} \frac{\left(x^p - j^p\right)^f \left(k^p - x^p\right)^g m(x)}{x^{(f+g)p}} \,dx$.
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Key Findings & Data:Through this equality, new integral inequalities were established, and novel upper bounds were obtained with the aid of Euler's beta and hypergeometric functions.
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Conclusion & Impact:The results provided new inequalities for the class of classical convex functions and the class of harmonic convex functions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$P-$convex function · $s-p-$convex function · harmonically convex function
Abstract
In this study, new lemmas on $p-$convex and $s-p-$convex functions were derived utilizing the integral $\int_{j}^{k} \frac{\left(x^p - j^p\right)^f \left(k^p - x^p\right)^g m(x)}{x^{(f+g)p}} \,dx$. Through this equality, new integral inequalities were established, and novel upper bounds were obtained with the aid of Euler's beta and hypergeometric functions. The results provided new inequalities for the class of classical convex functions and the class of harmonic convex functions.
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Cite This Article
Turhan, S., Kılıç, A., İşcan, İ. (2025). New integral inequalities involving p-convex and s-p-convex functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 74 Issue: 1. https://doi.org/10.31801/cfsuasmas.1448993