Affiliation:
1. Department of Mathematics, Faculty of Sciences , Ibn Tofail University , Morocco
Abstract
Abstract
All paper is related with the non-zero continuous solutions f : G → ℂ of the functional equation
f
(
x
σ
(
y
)
)
+
f
(
τ
(
y
)
x
)
=
2
f
(
x
)
f
(
y
)
,
x
,
y
∈
G
,
$${\rm{f}}({\rm{x}}\sigma ({\rm{y}})) + {\rm{f}}(\tau ({\rm{y}}){\rm{x}}) = 2{\rm{f}}({\rm{x}}){\rm{f}}({\rm{y}}),\;\;\;\;\;{\rm{x}},{\rm{y}} \in {\rm{G}},$$
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:
Reference11 articles.
1. [1] A. Chahbi, B. Fadli, S. Kabbaj, A generalization of the symmetrized multiplicative Cauchy equation, Acta Math. Hung., 149 (2016), 170–176.
2. [2] W. Chojnacki, On some functional equation generalizing Cauchy’s and d’Alembert’s functional equations, Colloq. Math., 55 (1988), 169–178.
3. [3] W. Chojnacki, On group decompositions of bounded cosine sequences, Studia Math., 181 (2007), 61–85.
4. [4] W. Chojnacki, On uniformly bounded spherical functions in Hilbert space, Aequationes Math., 81 (2011), 135–154.
5. [5] Iz. EL-Fassi, A. Chahbi, S. Kabbaj, The Solution of a class functional equations on semi-groups, Filomat, to appear.