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Coinciding Mean of the Two Symmetries on the Set of Mean Functions (CROSBI ID 322830)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Mihoković, Lenka Coinciding Mean of the Two Symmetries on the Set of Mean Functions // Axioms, 12 (2023), 3; 238, 15. doi: 10.3390/axioms12030238

Podaci o odgovornosti

Mihoković, Lenka

engleski

Coinciding Mean of the Two Symmetries on the Set of Mean Functions

On the set $\mathcal M$ of mean functions, the symmetric mean of $M$ with respect to mean $M_0$ can be defined in several ways. The first one is related to the group structure on $\mathcal M$, and the second one is defined trough Gauss' functional equation. In this paper, we provide an answer to the open question formulated by B.\ Farhi about the matching of these two different mappings called symmetries on the set of mean functions. Using techniques of asymptotic expansions developed by T.\ Buri\'c, N.\ Elezovi\'c, and L.\ Mihokovi\'c (Vuk\v si\'c), we discuss some properties of such symmetries trough connection with asymptotic expansions of means involved. As a result of coefficient comparison, a new class of means was discovered, which interpolates between harmonic, geometric, and arithmetic mean.

mean ; asymptotic expansion ; symmetry ; Catalan numbers

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Podaci o izdanju

12 (3)

2023.

238

15

objavljeno

2075-1680

10.3390/axioms12030238

Povezanost rada

Matematika

Poveznice
Indeksiranost