Minkowski’s inequality for two variable difference means

Abstract

Abstract. We study Minkowski's inequalityand its reverse where D a b is the difference mean introduced by Stolarsky. We give necessary and sufficient conditions (concerning the parameters a, b) for the inequality above (and for its reverse) to hold.

On the homogenization of means

“…The first subfield is related to the extensive study of homogeneous means which includes comparison and characterization problems, invariance equations and Minkowski-and Hölder-type inequalities (cf. [2], [3], [4], [13], [14], [21], [23], [25], [26], [28], [30]). The postulated domain of homogeneous means is usually the set of positive numbers and the means considered are power means, Gini means, Stolarsky means, symmetric polynomial means, counter-harmonic means, etc.…”

The Log-Convexity of Another Class of One-Parameter Means and Its Applications

“…Applying unified comparison theorem given in [22], a more generalized comparison problem for more extended means F (p, q; r, s; a, b) ≤ F (u, v; r, s; a, b) (a, b ∈ R + ) has been solved by Witkowski recently (see [36]). Other references involving these comparison problems can be found in [7], [3], [1], [2], [22], [17], [19], [6] Losonczi and Páles [15,16] established the Minkowski inequalities for the Stolarsky in 1996 and Gini means in 1998, respectively. Since symmetry of the two classes of means, and so they perfectly dealt with the bivariate convexities with respect to (a, b) actually.…”

A general Minkowski-type inequality for two variable Gini means

“…The first step in this direction is of course studying the case n = 2 and inequalities (2) and (4). This was done in the paper of Losonczi and Páles [LP96]. For brevity of notation, we use S a,b for S a,b;2 throughout the paper.…”

“…For brevity of notation, we use S a,b for S a,b;2 throughout the paper. Then the main result of [LP96] can be formulated as follows.…”