New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions
Universal Journal of Mathematics and Applications, vol.7, no.1, pp.30-37, 2024 (Scopus)
- Publication Type: Article / Article
- Volume: 7 Issue: 1
- Publication Date: 2024
- Doi Number: 10.32323/ujma.1397051
- Journal Name: Universal Journal of Mathematics and Applications
- Journal Indexes: Scopus
- Page Numbers: pp.30-37
- Keywords: Convex function, Fractional integrals, Milne type inequalities, Twice differentiable
- Open Archive Collection: AVESIS Open Access Collection
- Kocaeli University Affiliated: No
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, Hölder’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.