Schur-Convexity of Averages of Convex Functions

Applied Mathematics Letters, 2009

The Schur-convexity at the upper and lower limits of the integral for the mean of a convex function is researched. As applications, a form with a parameter of Stolarsky's mean is obtained and a relevant double inequality that is an extension of a known inequality is established.

2006

Two new means of two variables are defined by the hyperbolic and the arc-hyperbolic function composite function, and their Schur-convex and Schur-Geometric convex properties are discussed. As application, a new chain of inequalities is established.

2003

Let M : (0, ∞) 2 → (0, ∞) be a homogeneous strict mean such that the function h := M (·, 1) is twice dierentiable and 0 = h (1) = 1. It is shown that if there exists an M -ane function, continuous at a point which is neither constant nor linear, then M must be a weighted power mean. Moreover the homogeneity condition of M can be replaced by M -convexity of two suitably chosen linear functions. With the aid of iteration groups, some generalizations characterizing the weighted quasi-arithmetic means are given. A geometrical aspect of these results is discussed.

2012

In this paper, we establish some integral inequalities of Hermite-Hadamard type, in the framework of Borel probability measures.

2012

The authors establish some new inequalities for differentiable convex functions, which are similar to the celebrated Hermite-Hadamard's integral inequality for convex functions, and apply these inequalities to construct inequalities for special means of two positive numbers.

Journal of Convex Analysis

A set A will be said convexly majorized by a set B if the integral mean of any convex function over A is not exceeding its mean over B. Sufficient conditions and necessary conditions are presented about this relation. Methods are introduced which generate such sets A and B.

Journal of Mathematical Inequalities, 2007

The Schur-convexity on the upper and the lower limit of the integral for a mean of the convex function is researched. As applications, a generalized logarithmic mean with a parameter is obtained and a relevant double inequality that is a extension of the known inequality is established.

Analysis, 2012

In the paper, the authors discuss the Schur-harmonic convexity on .0; 1/ .0; 1/ for differences of some famous means, such as the arithmetic, geometric, harmonic, root-square means, and the like, and obtain some inequalities related to differences of means.

Applied Mathematics E-Notes, 2010

The Schur-geometric convexity in (0, ∞) × (0, ∞) for the difference of some famous means such as arithmetic mean, geometric mean, harmonic mean, rootsquare mean, etc. is discussed. Some inequalities related to the difference of means are obtained.

Miskolc Mathematical Notes, 2020

In this paper, we prove Hermite-Hadamard inequality for uniformly convex, uniformly s-convex functions. Also, we obtain Hermite Hadamard inequality for fractional integral by using these functions. Finally, some applications of these inequalities are given.