SciELO - Scientific Electronic Library Online

vol.38 issue2Further results on 3-product cordial labelingA sine type functional equation on a topological group author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • On index processCited by Google
  • Have no similar articlesSimilars in SciELO
  • On index processSimilars in Google


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

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


The integral sine addition law

D. Zeglami1 

M. Tial2 

S. Kabbaj3 

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

2Ibn Tofail University, Department of Mathematics, Faculty of Sciences, BP: 14000. Kenitra, Morocco. e-mail:

3Ibn Tofail University, Department of Mathematics, Faculty of Sciences, BP: 14000. Kenitra, Morocco. e-mail:


In the present paper we determine, in terms of characters and additive functions, the solutions of the integral functional equation for the sine addition law

(G f(xyt)dµ(t) = f(x)g(y) + g(x)f(y), x, y ∈ G,

where G is a locally compact Hausdorff group and µ is a regular, compactly supported, complex-valued Borel measure on G. Some consequences of this result and an example are presented.

Keywords: Functional equation; Sine and cosine addition laws; Character; Borel measure.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


The authors would like to express their most sincere gratitude to the referee for a number of constructive comments which have led to essential improvement of the paper.


[1] J. Aczél, Lectures on Functional Equations and Their Applications. Mathematics in Science and Engineering, vol. 19. Academic Press, New York, xx+510, (1966). [ Links ]

[2] J. K. Chung, Pl. Kannappan, C. T. Ng, A generalization of the cosinesine functional equation on groups. Linear Algebra Appl. 66, pp. 259-277, (1985). [ Links ]

[3] B. R. Ebanks, H. Stetkær, d’Alembert’s other functional equation on monoids with an involution. Aequationes Math. 89 (1), pp. 187-206, (2015). [ Links ]

[4] B. Fadli, D. Zeglami, S. Kabbaj, The generalized Van Vleck’s equation on locally compact groups. Proyecciones J. of Math., 36 (4), pp. 545- 566, (2017). [ Links ]

[5] B. Fadli , D. Zeglami , S. Kabbaj , An integral functional equation on groups under two measures. Proyecciones J. of Math. , 37 (3), pp. 565-581, (2018). [ Links ]

[6] Pl. Kannappan, Functional Equations and Inequalities with Applications. Springer, New York, 39-02 (39Bxx), (2009). [ Links ]

[7] Th. A. Poulsen, H. Stetkær, On the trigonometric subtraction and addition formulas. Aequationes Math. 59 (1), pp. 84-92 (2000). [ Links ]

[8] H. Stetkær , ”Functional equations on groups”. World Scientific Publishing Company, Singapore, (2013). [ Links ]

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

[10] H. Stetkær , The cosine addition law with an additional term, Aequationes Math. 90 (6), pp. 1147-1168, (2016). [ Links ]

[11] L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific Publishing Company, Singapore -New Jersey -London -Hong Kong, (1991). [ Links ]

[12] E. B. Van Vleck, A functional equation for the sine. Ann. of Math., Second Series, 11 (4), pp. 161-165, (1910). [ Links ]

[13] D. Zeglami , B. Fadli , S. Kabbaj , Harmonic analysis and generalized functional equations for the cosine, Adv. Pure Appl. Math. 7 (1), pp. 41-49, (2016). [ Links ]

[14] D. Zeglami , B. Fadli , Integral functional equations on locally compact groups with involution, Aequationes Math. 90 (5), pp. 967-982, (2016). [ Links ]

[15] D. Zeglami , Some functional equations related to number theory, Acta Math. Hungar. 149, no. 2, pp. 490-508, (2016). [ Links ]

[16] D. Zeglami , M. Tial, S. Kabbaj , The integral cosine addition and sine subtraction laws, Results Math. 73, no.3, 97, (2018). [ Links ]

Received: February 2017; Accepted: January 2019

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License