On Gautschi's harmonic mean inequality for the gamma function

A harmonic mean inequality for the digamma function and related results

We present some inequalities and a concavity property of the digamma function ψ = Γ′/Γ, where Γ denotes Euler’s gamma function. In particular, we offer a new characterization of Euler’s constant γ = 0.57721.... We prove that −γ is the minimum of the harmonic mean of ψ(x) and ψ(1/x) for x > 0. Mathematics Subject Classification (2010). 33B15, 39B62, 41A44.

A Note on a Gamma Function Inequality

The aim of this article is to present new inequalities which improve some gamma function inequalities of H. Alzer, Á. Baricz and N. Elezović et al. Mathematics subject classification (2000): 26D07, 33B15.

A Double Inequality for Gamma Function

On generalized Hermite-Hadamard inequality for generalized convex function

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

An Arithmetic-Geometric-Harmonic Mean Inequality Involving Hadamard Products

Given matrices of the same size, A = a ij ] and B = b ij ], we deene their Hadamard Product to be A B = a ij b ij ]. We show that if x i > 0 and q p 0 then the n n matrices q j # are positive deenite and relate these facts to some matrix valued arithmetic-geometric-harmonic mean inequalities-some of which involve Hadamard products and others unitarily invariant norms. It is known that if A is p...