On a metric topology on the set of bivariate means

Mustapha Raïssouli; Mohamed Chergui

doi:10.2478/ausm-2022-0010

.blurhash-client-img { display: none !important; }

On a metric topology on the set of bivariate means

Acta Universitatis Sapientiae, Mathematica

Volume 14 (2022): Issue 1 (November 2022)

By: Mustapha Raïssouli and Mohamed Chergui

Open Access

|Nov 2022

Abstract

In this paper, we define a distance d on the set ℳ of bivariate means. We show that (ℳ, d) is a bounded complete metric space which is not compact. Other algebraic and topological properties of (ℳ, d) are investigated as well.

References

[1] K. M. R. Audenaert, In-betweenness, a geometrical monotonicity property for operator means, Linear Algebra Appl, 16th ILAS Conference Proceedings, 438/4 (2013), 1769–1778.10.1016/j.laa.2011.02.051
Search in Google Scholar Back to article
[2] J. M. Borwein and P. B. Borwein, Pi and the AGM, A study in Analytic Number Theory and Computational Complexity, John Wiley and Sons Inc., New York, 1987.
Search in Google Scholar Back to article
[3] J. M. Borwein and P. B. Borwein, The way of all means, Amer. Math. Monthly, 94/6 (1987), 519–522.10.1080/00029890.1987.12000676
Search in Google Scholar Back to article
[4] P. S. Bullen, Handbook of Means and their Inequalities, Mathematics and its Applications, Springer, Second edition, 1987.
Search in Google Scholar Back to article
[5] A. L. Cauchy, Cours d’Analyse de l’Ecole Royale Polytechnique, 1ere Partie: Analyse Algébrique. Imprimerie Royale, Paris, 1821.
Search in Google Scholar Back to article
[6] T. H. Dinh, B. K. T. Vo, T. Y. Tam, In-sphere property and reverse inequalities for matrix means, Electron. J. Linear Algebra, 35/1 (2019), 35–41.10.13001/1081-3810.3728
Search in Google Scholar Back to article
[7] B. Farhi, Algebraic and topological structures on the set of means functions and generalization of the AGM mean, Colloquium Mathematicum, 132 (2013), 139–149.10.4064/cm132-1-11
Search in Google Scholar Back to article
[8] W. Janous, A note on generalized Heronian means, Math. Inequal. Appl. 4/3 (2001), 369–375.10.7153/mia-04-35
Search in Google Scholar Back to article
[9] M. Raïssouli and M. Chergui, On some inequalities involving three or more means, Abstract and Applied Analysis, (2016), Art. ID 1249604, 8 pages.10.1155/2016/1249604
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/ausm-2022-0010 | Journal eISSN: 2066-7752

Journal RSS Feed

Language: English

Page range: 147 - 159

Submitted on: Feb 16, 2021

Published on: Nov 18, 2022

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Related subjects:

© 2022 Mustapha Raïssouli, Mohamed Chergui, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Previous article Volume 14 (2022): Issue 1 (November 2022)Next article