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Solution of a functional equation on compact groups using Fourier analysis

Abdellatif ChahbiBrahim FadliSamir Kabbaj — 2015

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

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

Linear maps preserving A -unitary operators

Abdellatif ChahbiSamir KabbajAhmed Charifi — 2016

Mathematica Bohemica

Let be a complex Hilbert space, A a positive operator with closed range in ( ) and A ( ) the sub-algebra of ( ) of all A -self-adjoint operators. Assume φ : A ( ) onto itself is a linear continuous map. This paper shows that if φ preserves A -unitary operators such that φ ( I ) = P then ψ defined by ψ ( T ) = P φ ( P T ) is a homomorphism or an anti-homomorphism and ψ ( T ) = ψ ( T ) for all T A ( ) , where P = A + A and A + is the Moore-Penrose inverse of A . A similar result is also true if φ preserves A -quasi-unitary operators in both directions such that there exists an...

Stability of generalized quadratic functional equation on a set of measure zero

Youssef AribouHajira DimouAbdellatif ChahbiSamir Kabbaj — 2015

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

In this paper we prove the Hyers-Ulam stability of the following K-quadratic functional equation [...] where E is a real (or complex) vector space. This result was used to demonstrate the Hyers-Ulam stability on a set of Lebesgue measure zero for the same functional equation.

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