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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.2 Antofagasta jun. 2019

http://dx.doi.org/10.4067/S0716-09172019000200221 

Articles

A sine type functional equation on a topological group

D. Zeglami1 

S. Kabbaj2 

M. Tial3 

1Moulay Ismail University, Department of Mathematics, E.N.S.A.M, B. P: 15290 Al Mansour, Meknes, Morocco. e-mail : zeglamidriss@yahoo.fr

2Ibn Tofail University, Department of Mathematics, Faculty of Sciences, B. P. : 14000. Kenitra, Morocco. e-mail : samkabbaj@yahoo.fr

3Ibn Tofail University, Department of Mathematics, Faculty of Sciences, B. P. : 14000. Kenitra, Morocco. e-mail : tialmohamed@gmail.com

Abstract

In [13] H. Stetkær obtained the complex valued solutions of the functional equation

f(xyz0)f(xy−1z0) = f(x)2 − f(y)2, x, y ∈ G,

where G is a topological group and z0 ∈ Z(G) (the center of G). Our main goal is first to remove this restriction and second, when G is 2-divisible and abelian, we will investigate the superstability of the above functional equation.

Keywords: Sine functional equation; Character; Additive map; Superstability

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgement.

The authors wishe to thank the referee for a number of constructive comments which have led to essential improvement of the paper. We are indebted to Professor Henrik Stetkær for a helpful conversation which contributed to the first part of this article.

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Received: April 2017; Accepted: March 2019

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