Affiliation:
1. Department of Mathematics , E.N.S.A.M, Moulay ISMAÏL University , B.P: 15290 Al Mansour , Meknès , Morocco
Abstract
Abstract
The aim of this paper is to characterize the solutions Φ : G → M
2(ℂ) of the following matrix functional equations
Φ
(
x
y
)
+
Φ
(
σ
(
y
)
x
)
2
=
Φ
(
x
)
Φ
(
y
)
,
x
,
y
,
∈
G
,
{{\Phi \left( {xy} \right) + \Phi \left( {\sigma \left( y \right)x} \right)} \over 2} = \Phi \left( x \right)\Phi \left( y \right),\,\,\,\,\,\,x,y, \in G,
and
Φ
(
x
y
)
−
Φ
(
σ
(
y
)
x
)
2
=
Φ
(
x
)
Φ
(
y
)
,
x
,
y
,
∈
G
,
{{\Phi \left( {xy} \right) - \Phi \left( {\sigma \left( y \right)x} \right)} \over 2} = \Phi \left( x \right)\Phi \left( y \right),\,\,\,\,\,\,x,y, \in G,
where G is a group that need not be abelian, and σ : G → G is an involutive automorphism of G. Our considerations are inspired by the papers [13, 14] in which the continuous solutions of the first equation on abelian topological groups were determined.
Reference17 articles.
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5. [5] B. Fadli, D. Zeglami, and S. Kabbaj, A variant of Wilson’s functional equation, Publ. Math. Debrecen 87 (2015), no. 3-4, 415–427.
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