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Proyecciones (Antofagasta)
Print version ISSN 0716-0917
Proyecciones (Antofagasta) vol.38 no.2 Antofagasta June 2019
http://dx.doi.org/10.4067/S0716-09172019000200221
Articles
A sine type functional equation on a topological group
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
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
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
This is an open-access article distributed under the terms of the Creative Commons Attribution License
