A simple proof of monotonicity for Stolarsky and Gini means
A solution of an open problem concerning Lagrangian mean-type mappings
The problem of invariance of the geometric mean in the class of Lagrangian means was considered in [Głazowska D., Matkowski J., An invariance of geometric mean with respect to Lagrangian means, J. Math. Anal. Appl., 2007, 331(2), 1187–1199], where some necessary conditions for the generators of Lagrangian means have been established. The question if all necessary conditions are also sufficient remained open. In this paper we solve this problem.
A two-sided estimate of .
A variant of Jensen's inequality.
A variant of Jessen's inequality and generalized means.
Accentuate the negative
A survey of mean inequalities with real weights is given.
Affine and convex functions with respect to the logarithmic mean
The class of all functions f:(0,∞) → (0,∞) which are continuous at least at one point and affine with respect to the logarithmic mean is determined. Some related results concerning the functions convex with respect to the logarithmic mean are presented.
Algebraic and topological structures on the set of mean functions and generalization of the AGM mean
We present new structures and results on the set of mean functions on a given symmetric domain in ℝ². First, we construct on a structure of abelian group in which the neutral element is the arithmetic mean; then we study some symmetries in that group. Next, we construct on a structure of metric space under which is the closed ball with center the arithmetic mean and radius 1/2. We show in particular that the geometric and harmonic means lie on the boundary of . Finally, we give two theorems...
An algorithmic determination of optimal measure from data and some applications.
An extension of Stolarsky means.
An extension of Stolarsky means to the multivariable case.
An extension of the Hermite-Hadamard inequality and an application for Gini and Stolarsky means.
An improved Hardy-Rellich inequality with optimal constant.
An inequality of Ostrowski type via Pompeiu's mean value theorem.
An optimal double inequality between power-type Heron and Seiffert means.
An optimal double inequality for means.
Approaching the power logarithmic and difference means by iterative algorithms involving the power binomial mean.