Turkish Journal of Science
Journal license

Journal

Turkish Journal of Science


Volume
& Issue

Volume 10, Issue 2


Published
on

June 16, 2025


Pages

59-72


DOI

Article

Steffensen-Type Integral Inequalities for Functions with s-Convex Absolute n-th Derivatives


Authors

Sevgi SAHIN Affiliation:
Bandırma Onyedi Eylu¨l University, Graduate School, Balıkesir, Tu¨rkiye
and Alper EKINCI Affiliation:
Bandırma Onyedi Eylul University, Bandırma Vocational School, Balıkesir, Turkiye


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

Published by: Engineering Journals

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