Turkish Journal of Science
Journal license

Journal

Turkish Journal of Science


Volume
& Issue

Volume 9, Issue 1


Published
on

April 25, 2024


Pages

68-79


DOI

Article

Fractional Newton-Type Inequalities Involving s-Convex Functions

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Authors

Davut ALEMDAR Affiliation:
Department of Mathematics, Faculty of Science and Arts, Du¨zce University, Du¨zce 81620, Tu¨rkiye
, Hasan KARA Affiliation:
Department of Mathematics, Faculty of Science and Arts, Du¨zce University, Du¨zce 81620, Tu¨rkiye
and Huseyin BUDAK Affiliation:
Department of Mathematics, Faculty of Science and Arts, Du¨zce University, Du¨zce 81620, Tu¨rkiye


Abstract

In this paper, we present a novel method to examine Newton-type inequalities for s-convex functions using Riemann-Liouville fractional integrals. Specifically, we establish new fractional Newton- type inequalities by employing s-convex functions. The s-convexity property is extensively utilized to derive these inequalities. Additionally, we make use of the Holder inequality and the power-mean inequality to further strengthen our results. These new inequalities offer a more generalized perspective compared to classical inequalities, highlighting the significant role of s-convexity in modern mathematical analysis.


Keywords

Newton-type inequalities, convex functions, Ho¨lder inequality, power-mean inequality.


Citation

Alemdar, D., Kara, H., & Budak, H. (2024). Fractional newton-type inequalities involving s-convex functions. Turkish Journal of Science, 9(1), 68–79. https://doi.org/10.66833/TJOS-2024-0007

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