We study the following Minkowski-type inequality (*) Sa0,b0(x1 + y1,x2 + y2) ≤ Sa1,b1 (x1,x2) + Sa2,b2 (y1,y2) (x1,x2,y1,y2 ∈ ℝ+), where Sa,b is the two variable Gini mean defined by (Formula Presented) The case when a0 = a1 = a2 and b0 = b1 = b2 was investigated by LOSONCZI-PÁLES [LP96]. Generalizing their result, we give necessary and sufficient conditions (concerning the parameters ai,bi, ∈ ℝ) for the inequality above to hold. As a consequence of this result, it turns out that any inequality of the form (*) is weakening of an analogous inequality where all the participating means are equal to each other.
|Number of pages||14|
|Publication status||Published - Dec 1 2000|
- Gini means
- Minkowski inequality
- Two variable homogeneous means
ASJC Scopus subject areas