Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Mulholland's inequality


Authors: Witold Jarczyk and Janusz Matkowski
Journal: Proc. Amer. Math. Soc. 130 (2002), 3243-3247
MSC (2000): Primary 39B72, 26D15; Secondary 26A51
Published electronically: June 11, 2002
MathSciNet review: 1913002
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: H.P. Mulholland has presented a sufficient condition for a generalization of the Minkowski inequality and another such condition was given by R.M. Tardiff. We show that Mulholland's condition implies Tardiff's, but that the converse is false.


References [Enhancements On Off] (What's this?)

  • [1] Marek Kuczma, An introduction to the theory of functional equations and inequalities, Prace Naukowe Uniwersytetu Śląskiego w Katowicach [Scientific Publications of the University of Silesia], vol. 489, Uniwersytet Śląski, Katowice; Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1985. Cauchy’s equation and Jensen’s inequality; With a Polish summary. MR 788497 (86i:39008)
  • [2] Janusz Matkowski, 𝐿^{𝑝}-like paranorms, Selected topics in functional equations and iteration theory (Graz, 1991), Grazer Math. Ber., vol. 316, Karl-Franzens-Univ. Graz, Graz, 1992, pp. 103–138. MR 1226468 (94g:39010)
  • [3] J. Matkowski, On a generalization of Mulholland’s inequality, Abh. Math. Sem. Univ. Hamburg 63 (1993), 97–103. MR 1227867 (94g:26032), http://dx.doi.org/10.1007/BF02941335
  • [4] H. P. Mulholland, On generalizations of Minkowski’s inequality in the form of a triangle inequality, Proc. London Math. Soc. (2) 51 (1950), 294–307. MR 0033865 (11,503f)
  • [5] A. Sklar, Remark and Problem, Report of meeting, 37th International Symposium on Functional Equations (Huntington, 1999), Aequationes Math. 60 (2000), 187-188.
  • [6] Robert M. Tardiff, On a generalized Minkowski inequality and its relation to dominates for 𝑡-norms, Aequationes Math. 27 (1984), no. 3, 308–316. MR 762688 (86j:26013), http://dx.doi.org/10.1007/BF02192679

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 39B72, 26D15, 26A51

Retrieve articles in all journals with MSC (2000): 39B72, 26D15, 26A51


Additional Information

Witold Jarczyk
Affiliation: Institute of Mathematics, Technical University, Podgórna 50, PL–65–246 Zielona Góra, Poland – and – Institute of Mathematics, Silesian University, Bankowa 14, PL–40–007 Katowice, Poland
Email: w.jarczyk@im.uz.zgora.pl

Janusz Matkowski
Affiliation: Institute of Mathematics, Technical University, Podgórna 50, PL–65–246 Zielona Góra, Poland – and – Institute of Mathematics, Silesian University, Bankowa 14, PL–40–007 Katowice, Poland
Email: j.matkowski@im.uz.zgora.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06708-4
PII: S 0002-9939(02)06708-4
Keywords: Generalizations of the Minkowski inequality, Mulholland's inequality, convex functions, geometrically convex functions
Received by editor(s): June 4, 2001
Published electronically: June 11, 2002
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society