New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions

Year 2024, Volume: 7 Issue: 1, 30 - 37, 18.03.2024

Henok Desalegn Desta , Hüseyin Budak , Hasan Kara

https://doi.org/10.32323/ujma.1397051

Cited By: 8

Abstract

This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, H\"{o}lder's inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples.

Keywords

Convex function, Fractional integrals, Milne type inequalities, Twice differentiable

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