Generalized Steffensen Means

generalized steffensen means

On the Jensen-Steffensen inequality for generalized convex functions

Jensen–Steffensen type inequalities for P -convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen–Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.

Correction to "generalized Means"

The purpose of this note is to correct a mistake in the paper entitled Generalized means, which appeared in these Transactions [4]. At the same time, it may be appropriate to report the state of some problems raised there. 1. In §7 of [4] it is asserted that the set of means forms a compact set in the weak operator topology. I am indebted to S. P. Lloyd, of the Bell Telephone Laboratories, for ...

A Generalized Singular Value Inequality for Heinz Means

In this paper we will generalize a singular value inequality that was proved before. In particular we obtain an inequality for numerical radius as follows: begin{equation*} 2 sqrt{t (1-t)} omega(t A^{nu}B^{1-nu}+(1-t)A^{1-nu}B^{nu}) leq omega(t A + (1- t) B), end{equation*} where, $ A $ and $ B $ are positive semidefinite matrices, $ 0 leq t leq 1 $ and $ 0 leq nu leq frac{3}{2}.$

A Steffensen Type Inequality

Steffensen’s inequality deals with the comparison between integrals over a whole interval [a, b] and integrals over a subset of [a, b]. In this paper we prove an inequality which is similar to Steffensen’s inequality. The most general form of this inequality deals with integrals over a measure space. We also consider the discrete case.

Inequalities for Generalized Logarithmic Means

For p ∈ R, the generalized logarithmic mean Lp of two positive numbers a and b is defined as Lp a, b a, for a b, LP a, b b 1 − a 1 / p 1 b − a 1/p , for a/ b, p / − 1, p / 0, LP a, b b − a / log b − loga , for a/ b, p −1, and LP a, b 1/e b/a 1/ b−a , for a/ b, p 0. In this paper, we prove that G a, b H a, b 2L−7/2 a, b , A a, b H a, b 2L−2 a, b , and L−5 a, b H a, b for all a, b > 0, and the co...