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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minkowski's inequality
for two variable difference means


Authors: László Losonczi and Zsolt Páles
Journal: Proc. Amer. Math. Soc. 126 (1998), 779-789
MSC (1991): Primary 26D15, 26D07
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Abstract: We study Minkowski's inequality

\begin{displaymath}D_{a\,b}(x_1+x_2, y_1+y_2)\le D_{a\,b}(x_1, y_1)+D_{a\,b}(x_2,y_2) \quad(x_1,x_2, y_1,y_2\in \mathbb R_+) \end{displaymath}

and 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.


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Additional Information

László Losonczi
Affiliation: Department of Mathematics and Computer Science, Kuwait University, P.O.Box 5969 Safat, 13060 Kuwait
Email: losonczi@math-1.sci.kuniv.edu.kw

Zsolt Páles
Affiliation: Institute of Mathematics, Lajos Kossuth University \ H-4010 Debrecen, Pf. 12, Hungary
Email: pales@math.klte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04125-2
PII: S 0002-9939(98)04125-2
Keywords: Difference means, Minkowski's inequality
Received by editor(s): April 3, 1996
Received by editor(s) in revised form: September 3, 1996
Additional Notes: Research of the first author supported by Kuwait University Grant SM 145 and research of the second author by the Hungarian National Foundation for Scientific Research (OTKA), Grant No.\ T-016846.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society