Abstract
We generalize an integral Jensen–Mercer inequality to the class of n-convex functions using Fink’s identity and Green’s functions. We study the monotonicity of some linear functionals constructed from the obtained inequalities using the definition of n-convex functions at a point.
Highlights
We study the monotonicity of some linear functionals constructed from the obtained inequalities using the definition of n-convex functions at a point
The main goal of this paper is to present generalizations of inequality (4) to the class of n-convex functions
We start with two identities which are very useful in obtaining generalizations of inequality (4) to the class of n-convex functions
Summary
Generalizations of the Jensen–Mercer Inequality via Fink’s Identity. For a convex function f : I → R, real numbers x1, . Xn ∈ I and positive real numbers w1, . Wn, where Wn = ∑in=1 wi, is one of the most important inequalities in many areas of mathematics and other areas of science. Many other inequalities can be derived from it and there are numerous of its variants, generalizations and refinements (see, for example [1,2]). One of these variants is the so-called Jensen–Mercer inequality, ∑ f α + β
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