# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Properties of mappings related to the Minkowski inequality. (English) Zbl 1232.26033
Summary: We obtain properties of several mappings which are arisen from the Minkowski inequality. We investigate superadditivity (subadditivity) and monotonicity of those functions, and give some refinements of the Minkowski inequality and the Hölder inequality.
##### MSC:
 26D15 Inequalities for sums, series and integrals of real functions 28A25 Integration with respect to measures and other set functions
##### References:
 [1] Dragomir S.S., Pečarić J.E., Persson L.E.: Properties of some functionals related to Jensen’s inequality. Acta Math. Hungar 70(1–2), 129–143 (1996) · Zbl 0847.26013 · doi:10.1007/BF00113918 [2] E. H. Lieb and M. Loss, Analysis, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, 2001. [3] McLaughlin H.W., Metcalf F.T.: The Minkowski and Tchebychef inequalities as functions of the index set. Duke Math. J. 35, 865–873 (1968) · Zbl 0183.05002 · doi:10.1215/S0012-7094-68-03594-1 [4] Pečarić J.E.: Improvements of H”older’s and Minkowski’s inequalities. Mat. Bilten 17, 69–74 (1993) [5] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex functions, partial orderings, and statistical applications, Academic Press Inc., 1992. [6] Vasić P.M., Pečarić J.E.: On the Hölder and some related inequalities. Rev. Anal. Numér. Théor. Approx. 25(48), 95–103 (1982) No 1