Generalized small-dimension lemma and d’Alembert type functional equation on compact groups

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Iz-iddine EL-Fassi ◽  
Abdellatif Chahbi
Keyword(s):  
Functional Equation ◽  
Small Dimension ◽  
Compact Groups

scholarly journals Solution of a functional equation on compact groups using Fourier analysis

2015 ◽  
Vol 69 (2) ◽  
pp. 9
Author(s):  
Abdellatif Chahbi ◽  
Brahim Fadli ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Fourier Transform ◽  
Fourier Analysis ◽  
Compact Group ◽  
Compact Groups ◽  
Continuous Solutions ◽  
Fixed Element ◽  
Continuous Automorphism

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 \(G\).

scholarly journals An extension of a variant of d’Alemberts functional equation on compact groups

2017 ◽  
Vol 9 (1) ◽  
pp. 45-52
Author(s):  
Iz-iddine EL-Fassi ◽  
Abdellatif Chahbi ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Compact Group ◽  
Compact Groups ◽  
Continuous Solutions ◽  
Continuous Automorphism

Abstract All paper is related with the non-zero continuous solutions f : G → ℂ of the functional equation $${\rm{f}}({\rm{x}}\sigma ({\rm{y}})) + {\rm{f}}(\tau ({\rm{y}}){\rm{x}}) = 2{\rm{f}}({\rm{x}}){\rm{f}}({\rm{y}}),\;\;\;\;\;{\rm{x}},{\rm{y}} \in {\rm{G}},$$ where σ; τ are continuous automorphism or continuous anti-automorphism defined on a compact group G and possibly non-abelian, such that σ2 = τ2 = id: The solutions are given in terms of unitary characters of G:

scholarly journals D'Alembert's functional equation on compact groups

2007 ◽  
Vol 1 (2) ◽  
pp. 221-226 ◽  
Author(s):  
Laszlo Szekelyhidi ◽  
Aleksandar S. Cvetkovic ◽  
Marija P. Stanic
Keyword(s):  
Functional Equation ◽  
Compact Groups ◽  
D’Alembert’S Functional Equation

The one-level functional equation of multi-rate loss systems

2003 ◽  
Vol 14 (2) ◽  
pp. 107-118 ◽  
Author(s):  
Harro L. Hartmann ◽  
Martin Knoke
Keyword(s):  
Functional Equation ◽  
Loss Systems ◽  
The One ◽  
Rate Loss

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

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