From a theorem of R. Ger and T. Kochanek to marginal joints of means
- 194 Downloads
We answer in the negative a problem posed in Daróczy (Report on 52nd International Symposium on Functional Equations. Aequat. Math., 2015) by the first author, in connection with a result of Ger and Kochanek (Colloq Math 115:87–99, 2009), and its generalization formulated in Daróczy et al. (Report on 52nd International Symposium on Functional Equations. Aequat. Math., 2015). A further generalization is posed as an open problem. Elaborating an idea of the construction of means presented in Examples 1.2 and 1.4 we come to the notion of marginal joints of means. It provides a pretty wide class of means extending two given means on adjacent intervals.
KeywordsMean Quasi-arithmetic mean Generalized Jensen’s equation Extension of means Marginal joint of means
Mathematics Subject ClassificationPrimary 26E60 Secondary 39B22
- 1.Aczél, J., Dhombres, J.: Functional equations in several variables. With applications to mathematics, information theory and to the natural and social sciences. In: Encyclopedia of Mathematics and its Applications, vol. 31. Cambridge University Press, Cambridge (1989)Google Scholar
- 3.Daróczy, Z.: On generalizations of Jensen’s functional equation (2015). (manuscript)Google Scholar
- 4.Daróczy, Z.: Problem. In: Report on 52nd International Symposium on Functional Equations. Aequat. Math. (2015). (in print)Google Scholar
- 5.Daróczy, Z., Jarczyk, J., Jarczyk, W.: Remark and problem. In: Report on 52nd International Symposium on Functional Equations. Aequat. Math. (2015). (in print)Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.