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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.37 no.3 Antofagasta Sept. 2018 


An integral functional equation on groups under two measures

B. Fadli1 

D. Zeglami2 

S. Kabbaj3 

1IBN Tofail University, Department of Mathematics, Faculty of Sciences, B. P. : 14000. Kenitra, Morocco e-mail :

2Moulay ISMAIL University, E. N. S. A. M, Department of Mathematics, B. P. : 15290 Al Mansour-MEKNES, Morocco, e-mail :

3IBN Tofail University, Department of Mathematics, Faculty of Sciences, B. P. : 14000. Kenitra, Morocco e-mail :


Let G be a locally compact Hausdorff group, let σ be a continuous involutive automorphism on G, and let μ, ν be regular, compactly supported, complex-valued Borel measures on G. We find the continuous solutions 𝑓 : G → C of the functional equation

in terms of continuous characters of G. This equation provides a common generalization of many functional equations (d’Alembert’s, Cauchy’s, Gajda’s, Kannappan’s, Stetkær’s, Van Vleck’s equations...). So, a large class of functional equations will be solved.

Keywords: Functional equation; Van Vleck; Kannappan; involutive automorphism; group character.

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[1] Badora, R.: On a joint generalization of Cauchy’s and d’Alembert’s functional equations. Aequationes Math. 43 (1), pp. 72-89, (1992). [ Links ]

[2] Fadli, B., Zeglami, D., Kabbaj, S.: A joint generalization of Van Vleck’s and Kannappan’s equations on groups. Adv. Pure Appl. Math. 6 (3), pp. 179-188, (2015). [ Links ]

[3] Gajda, Z.: A generalization of d’Alembert’s functional equation, Funkcial. Ekvac. 33 (1), pp. 69-77, (1990). [ Links ]

[4] Kannappan, PL.: A functional equation for the cosine. Can. Math. Bull. 11, pp. 495-498, (1968). [ Links ]

[5] Kannappan, PL.: Functional equations and inequalities with applications. Springer, New York, (2009). [ Links ]

[6] Perkins, A.M., Sahoo, P.K.: On two functional equations with involution on groups related to sine and cosine functions. Aequationes Math . 89 (5), pp. 1251-1263, (2015). [ Links ]

[7] Stetkær, H.: Functional equations on groups. World Scientific, Publishing Co, Singapore, (2013). [ Links ]

[8] Stetkær, H.: Van Vleck’s functional equation for the sine. Aequationes Math . 90 (1), pp. 25-34, (2016). [ Links ]

[9] Stetkær, H.: Kannappan’s functional equation on semigroups with involution. Semigroup Forum. 94 (1), pp. 17-30, (2017). [ Links ]

[10] Van Vleck, E.B.: A functional equation for the sine. Ann. Math. 7, pp. 161-165, (1910). [ Links ]

Accepted: May 2018; Received: November 2017

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