Article
Steffensen-Type Integral Inequalities for Functions with s-Convex Absolute n-th Derivatives
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Abstract
In this paper, we establish new Steffensen-type integral inequalities for functions whose absolute nth derivatives are s-convex in the second sense. By deriving an appropriate integral representation and employing inequalities such as Ho¨lder, power-mean, and Young, we obtain several explicit upper bounds expressed in terms of endpoint values of the absolute n-th derivative of f. The obtained results generalize Steffensen-type inequalities to the s-convex framework and provide a unified treatment of different analytical techniques within this setting.
Keywords
Hermite-Hadamard Inequality, Steffensen’s Inequality, s-Convex Functions, Young’s inequality.
Citation
Sahin, S. & Ekinci, A. (2025). Steffensen-type integral inequalities for functions with s-convex absolute n-th derivatives. Turkish Journal of Science, 10(2), 59–72. https://doi.org/10.66833/TJOS-2025-0006
S. Sahin and A. Ekinci, “Steffensen-type integral inequalities for functions with s-convex absolute n-th derivatives,” Turkish Journal of Science, vol. 10, no. 2, pp. 59–72, 2025, doi: 10.66833/TJOS-2025-0006.
Sahin S, Ekinci A. Steffensen-type integral inequalities for functions with s-convex absolute n-th derivatives. Turkish Journal of Science. 2025;10(2):59–72. doi:10.66833/TJOS-2025-0006.
Sahin, S. and Ekinci, A. (2025), ‘Steffensen-type integral inequalities for functions with s-convex absolute n-th derivatives’, Turkish Journal of Science, 10(2), pp. 59–72. Available at: https://doi.org/10.66833/TJOS-2025-0006.
Sahin, Sevgi, and Alper Ekinci. “Steffensen-type Integral Inequalities for Functions with S-convex Absolute N-th Derivatives.” Turkish Journal of Science, vol. 10, no. 2, 2025, pp. 59–72. https://doi.org/10.66833/TJOS-2025-0006.
Sahin, Sevgi, and Alper Ekinci. “Steffensen-type Integral Inequalities for Functions with S-convex Absolute N-th Derivatives.” Turkish Journal of Science 10, no. 2 (2025): 59–72. https://doi.org/10.66833/TJOS-2025-0006.
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Published by: Engineering Journals


