Geometric inequalities in harmonic analysis

Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means

Affine inequalities in harmonic analysis

We discuss two affine inequalities and their role in two specific problems in harmonic analysis. The aim is to clarify the role that affine inequalities may play in harmonic analysis rather than to present any definitive results.

Geometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function

Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.

A Note on the Weighted Harmonic–geometric–arithmetic Means Inequalities

In this note, we derive non trivial sharp bounds related to the weighted harmonicgeometric-arithmetic means inequalities, when two out of the three terms are known. As application, we give an explicit bound for the trace of the inverse of a symmetric positive definite matrix and an inequality related to the coefficients of polynomials with positive roots. Mathematics subject classification (201...

Best Possible Inequalities among Harmonic, Geometric, Logarithmic and Seiffert Means

In this paper, we find the greatest value α and the least values β , p , q and r in (0,1/2) such that the inequalities L(αa+ (1−α)b,αb+ (1−α)a) < P(a,b) < L(βa + (1− β)b,βb + (1− β)a) , H(pa + (1− p)b, pb + (1− p)a) > G(a,b) , H(qa+ (1− q)b,qb +(1− q)a) > L(a,b) , and G(ra+(1− r)b,rb+(1− r)a) > L(a,b) hold for all a,b > 0 with a = b . Here, H(a,b) , G(a,b) , L(a,b) and P(a,b) denote the harmoni...