Next, we point out some applications of our results to give estimates for the approximation error of the integral function in the trapezoidal formula and for some inequalities related to special means of real numbers.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we introduce and study the concept of (s,P)-function and establish Hermite-Hadamard’s inequalities for this type of functions.
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Key Findings & Data:Also, we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is (s,P)-function by using Hölder and power-mean integral inequalities.
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Conclusion & Impact:Next, we point out some applications of our results to give estimates for the approximation error of the integral function in the trapezoidal formula and for some inequalities related to special means of real numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:s-convex function · P)-function · Hermite-Hadamard inequality
Abstract
In this paper, we introduce and study the concept of (s,P)-function and establish Hermite-Hadamard’s inequalities for this type of functions. Also, we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is (s,P)-function by using Hölder and power-mean integral inequalities. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral function in the trapezoidal formula and for some inequalities related to special means of real numbers.
Numan, S., İşcan, İ. (2022). On (s, P)-functions and related inequalities. Sigma Journal of Engineering and Natural Sciences, Volume: 40 Issue: 3. https://ajindex.com/articles/1632414