Minkowski’s inequality for two variable difference means
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- Proc. Amer. Math. Soc. 126 (1998), 779-789 Request permission
Abstract:
We study Minkowski’s inequality \[ D_{a b}(x_1+x_2, y_1+y_2)\le D_{a b}(x_1, y_1)+D_{a b}(x_2,y_2) \quad (x_1,x_2, y_1,y_2\in \mathbb R_+) \] 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.References
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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
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 779-789
- MSC (1991): Primary 26D15, 26D07
- DOI: https://doi.org/10.1090/S0002-9939-98-04125-2
- MathSciNet review: 1423317