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Solution of a functional equation on compact groups using Fourier analysis

100%

Chahbi A., Fadli B., Kabbaj S.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2015

tom 69

nr 2

Let \(G\) be a compact group, let \(n \in N\setminus \{0,1\}\) be a fixed element and let \(\sigma\) be a continuous automorphism on \(G\) such that \(\sigma^n=I\). Using the non-abelian Fourier transform, we determine the non-zero continuous solutions \(f:G \to C\) of the functional equation \[ f(xy)+\sum_{k=1}^{n-1}f(\sigma^k(y)x)=nf(x)f(y),\ x,y \in G,\] in terms of unitary characters of \(G\).

A solution of an open problem concerning Lagrangian mean-type mappings

100%

Głazowska D.

Open Mathematics

2011

tom 9

nr 5

1067-1073

The problem of invariance of the geometric mean in the class of Lagrangian means was considered in [Głazowska D., Matkowski J., An invariance of geometric mean with respect to Lagrangian means, J. Math. Anal. Appl., 2007, 331(2), 1187–1199], where some necessary conditions for the generators of Lagrangian means have been established. The question if all necessary conditions are also sufficient remained open. In this paper we solve this problem.

Ograniczanie wyników

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Open Mathematics

1 Chahbi A.

1 Fadli B.

1 Głazowska D.

1 Kabbaj S.

1 2015

1 2011

Wyniki wyszukiwania

Solution of a functional equation on compact groups using Fourier analysis

A solution of an open problem concerning Lagrangian mean-type mappings