FRACTIONAL MACLAURIN-TYPE INEQUALITIES FOR TWICE-DIFFERENTIABLE FUNCTIONS
Fatih Hezenci
Abstract
We prove an equality for twice-differentiable functions whose second derivatives in absolute value are convex. We use this, together with the Hölder and power-mean inequalities, to establish some Maclaurin-type inequalities for Riemann–Liouville fractional integrals. We conclude with some special cases.
Topics & Concepts
MathematicsDifferentiable functionType (biology)InequalityApplied mathematicsMathematical analysisPure mathematicsBiologyEcologyMathematical Inequalities and ApplicationsNonlinear Differential Equations AnalysisFunctional Equations Stability Results