Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications
Saad Ihsan Butt, Praveen Agarwal, Saba Yousaf, Juan L. G. Guirao
Abstract
Abstract In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.
Topics & Concepts
MathematicsJensen's inequalityConvex functionPure mathematicsRegular polygonType (biology)FractalFunction (biology)Harmonic functionMathematical analysisConvex analysisConvex optimizationGeometryBiologyEvolutionary biologyEcologyMathematical Inequalities and ApplicationsFunctional Equations Stability ResultsFractional Differential Equations Solutions