Expansion of a Bivariate Symmetric Mean in the Neighbourhood of the First Bisector

Bakir Farhi

doi:10.2478/tmmp-2026-0008

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

Expansion of a Bivariate Symmetric Mean in the Neighbourhood of the First Bisector

Tatra Mountains Mathematical Publications

Volume 92 (2026): Issue 1 (July 2026)

By: Bakir Farhi

Open Access

|Jun 2026

ACZÉL, J.—DHOMBRES, J.: Functional Equations in Several Variables. With Applications to Mathematics, Information Theory and to the Natural and Social Siences. Encyclopedia of Mathematics and its Applications. Vol. 31, Cambridge University Press, Cambridge, 1989.
Search in Google Scholar Back to article
ALZER, A.—RUSCHEWEYH, S.: On the intersection of two-parameter mean value families, Proc. Amer. Math. Soc. 129 (2001), no. 9, 2655–2662.
Search in Google Scholar Back to article
BORWEIN, J. M.—BORWEIN, P. B.: Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity. SIAM Review, 1988, 30, 530-533 Wiley, New York, 1987.
Search in Google Scholar Back to article
BULLEN, P. S.: Handbook of Means and Their Inequalities. Vol. 560, Springer Science & Business Media, 2013.
Search in Google Scholar Back to article
BURIĆ, T.—ELEZOVIĆ, N.: Computation and analysis of the asymptotic expansions of the compound means, Appl. Math. Comput. 303 (2017), 48–54.
Search in Google Scholar Back to article
ELEZOVIĆ, N.: Asymptotic inequalities and comparison of classical means,J.Math. Inequal. 9 (2015), 177–196.
Search in Google Scholar Back to article
ELEZOVIĆ, N.—VUKŠIĆ, L.: Asymptotic expansions and comparison of bivariate parameter means, Math. Inequal. Appl. 17 (2014), no. 4, 1225–1244.
Search in Google Scholar Back to article
ELEZOVIĆ, N.—VUKŠIĆ, L.: Asymptotic expansions of bivariate classical means and related inequalities, J. Math. Inequal. 8 (2014), no. 4, 707–724.
Search in Google Scholar Back to article
ELEZOVIĆ, N.—VUKŠIĆ, L.: Asymptotic expansions of integral means and applications to the ratio of gamma functions, Appl. Math. Comput. 235 (2014), 187–200.
Search in Google Scholar Back to article
FARHI, B.: Algebraic and topological structures on the set of mean functions and generalization of the AGM mean, Colloq. Math. 132 (2013), 139–149.
Search in Google Scholar Back to article
GINI, C.: Di una formula compressiva delle medie. Ammin. del Metron, 13 (1938), 3–22.
Search in Google Scholar Back to article
LEHMER, D. H.: On the compounding of certain means, J. Math. Anal. Appl. 36 (1971), 183–200.
Search in Google Scholar Back to article
MIHOKOVIĆ, L.: Coinciding mean of the two symmetries on the set of mean functions, Axioms 12 (2023), no. 3, 238.
Search in Google Scholar Back to article
STOLARSKY, K. B.: Generalizations of the logarithmic mean, Math. Mag. 48 (1975), no. 2, 87–92.
Search in Google Scholar Back to article

Authors

Metrics

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2026-0008 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

Journal RSS Feed

Language: English

Page range: 63 - 118

Submitted on: Jun 19, 2025

Accepted on: May 21, 2026

Published on: Jun 19, 2026

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

bivariate means,

series expansions of means,

comparison of means,

equivalence of means,

normal means,

additive means,

integral means,

Gauss arithmetic-geometric mean

Related subjects:

Mathematics,

General mathematics

© 2026 Bakir Farhi, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 92 (2026): Issue 1 (July 2026)