Pure mathematics

Mathematics

Fractal

Evolutionary biology

Biology

Regular polygon

Convex analysis

Convex optimization

Mathematical analysis

Function (biology)

Convex function

Jensen's inequality

Ecology

Geometry

Type (biology)

Harmonic function

Journal of Inequalities and Applications

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.

Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications