New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions
Henok Desalegn Desta, Hüseyin Budak, Hasan Kara
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.
Topics & Concepts
Differentiable functionInequalityConvexityMathematical proofType (biology)MathematicsConvex functionPure mathematicsRegular polygonJensen's inequalityCalculus (dental)Algebra over a fieldMathematical economicsMathematical analysisConvex optimizationConvex analysisGeometryEconomicsGeologyPaleontologyDentistryMedicineFinancial economicsMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsOptimization and Variational Analysis