On Mulholland’s inequality
HTML articles powered by AMS MathViewer
- by Witold Jarczyk and Janusz Matkowski
- Proc. Amer. Math. Soc. 130 (2002), 3243-3247
- DOI: https://doi.org/10.1090/S0002-9939-02-06708-4
- Published electronically: June 11, 2002
- PDF | Request permission
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
- 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
- Janusz Matkowski, $\textbf {L}^p$-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
- J. Matkowski, On a generalization of Mulholland’s inequality, Abh. Math. Sem. Univ. Hamburg 63 (1993), 97–103. MR 1227867, DOI 10.1007/BF02941335
- Morgan Ward and R. P. Dilworth, The lattice theory of ova, Ann. of Math. (2) 40 (1939), 600–608. MR 11, DOI 10.2307/1968944
- A. Sklar, Remark and Problem, Report of meeting, 37th International Symposium on Functional Equations (Huntington, 1999), Aequationes Math. 60 (2000), 187–188.
- 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, DOI 10.1007/BF02192679
Bibliographic 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
- Received by editor(s): June 4, 2001
- Published electronically: June 11, 2002
- Communicated by: Jonathan M. Borwein
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3243-3247
- MSC (2000): Primary 39B72, 26D15; Secondary 26A51
- DOI: https://doi.org/10.1090/S0002-9939-02-06708-4
- MathSciNet review: 1913002