Inequalities for arithmetic functions

Analysis, 2013
Summary: The authors introduce the notion of a geometric-arithmetically \(s\)-convex function, establish some Hermite-Hadamard type inequalities of this kind of functions, and apply their inequalities in order to construct inequalities for special means.
Shuang, Ye, Yin, Hong-Ping, Qi, Feng
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Some integral inequalities for arithmetically and geometrically convex functions of two variables

2022
A real convex function \(f\) is expressed by the arithmetic mean: if \(\mathcal{A}_\lambda(a,b)=\lambda a+(1-\lambda)b\) is the (weighted) arithmetic mean of two real numbers \(a\) and \(b\), then a function \(f\) is convex if and only if \(f(\mathcal{A}_\lambda(x,y))\leq \mathcal{A}_\lambda(f(x),f(y))\) for all \(x,y\) in the domain of \(f\).
Darvish, Vahid +3 more
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Inequalities of Hermite-Hadamard type for \(n\)-times differentiable arithmetic-harmonically functions

2022
Summary: In this work, by using an integral identity together with both the Hölder and the power-mean integral inequalities we establish several new inequalities for \(n\)-times differentiable arithmetic-harmonically-convex function. Then, using this inequalities, we obtain some new inequalities connected with means.
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convex function
mathematics
arithmetic functions

inequalities for sums, series and integrals
means
hölder inequality

fos: mathematics
hermite-hadamard inequality
convex functions