Abstract
The notion of set-valued means is introduced. Set-valued counterparts of the arithmetic, quasi-arithmetic and Lagrangian means are investigated and various properties of them are presented.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aczél, J., Dhombres, J.: Functional Equations in Several Variables with Applications to Mathematics, Information Theory and to the Natural and Social Sciences. Cambridge University Press, Cambridge (1989)
Aubin, J.-P., Frankowska, H.: Set-valued Analysis. Birkhäuser, Boston-Basel-Berlin (1990)
Beckenbach, B., Bellman, R.: An introduction to inequalities. Random House and Yale University (1961)
Bullen, P.S.: Handbook of Means and Their Inequalities. Kluwer, Dordrecht (2003)
Cauchy, A.L.: Cours D’analyse De L’École Royale Polytechnique, Ire Partie: Analyse Algébrique. Imprimérie Royale, Paris (1821)
Daróczy, Z., Páles, Z.: Gauss-composition of means and the solution of matkowski-sutô problem. Publ. Math. Debrecen 61, 157–218 (2002)
Elezović, N.: Asymptotic inequalities and comparison of classical means. J. Math. Ineq. 9, 177–196 (2015)
Jarczyk, J., Jarczyk, W.: Invariance of means. Aequat. Math. 92, 801–872 (2018)
Makó, J., Páles, Z.: The invariance of the atithmetic mean with respect to generalized quasi-arithmetic means. J. Math. Anal. Appl. 353, 8–23 (2009)
Matkowski, J.: Generalized weighted arithmetic means. In: Rassias, T., Brzdȩk, J. (eds.) Functional Equations in Mathematical Analysis, pp 563–582. Springer, New York (2012)
Nikodem, K.: K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. Łódz. Mat. 559(Rozprawy Nauk 114 Łódź), 1–75 (1989)
Toader, G., Costin, I.: Means in Mathematical Analysis. Bivariate Means. Mathematical Analysis and Its Applicatio Series. Academic Press, An imprint of Elsevier, London (2018)
Acknowledgements
The author express his gratitude to the anonymous referees for their careful reading and detailed comments which have improved the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Nikodem, K. Set-Valued Means. Set-Valued Var. Anal 28, 559–568 (2020). https://doi.org/10.1007/s11228-020-00532-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11228-020-00532-6