An integral functional equation on groups under two measures

  • B. Fadli IBN Tofail University.
  • D. Zeglami Moulay Ismail University.
  • S. Kabbaj IBN Tofail University.

Resumen

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.    

Biografía del autor

B. Fadli, IBN Tofail University.
Departamento de Matemáticas, Facultad de Ciencias.
D. Zeglami, Moulay Ismail University.
E. N. S. A. M., Departamento de Matemáticas.
S. Kabbaj, IBN Tofail University.
Departamento de Matemáticas. Facultad de Ciencias.

Citas

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[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).
[3] Gajda, Z.: A generalization of d’Alembert’s functional equation, Funkcial. Ekvac. 33 (1), pp. 69-77, (1990).
[4] Kannappan, PL.: A functional equation for the cosine. Can. Math. Bull. 11, pp. 495-498, (1968).
[5] Kannappan, PL.: Functional equations and inequalities with applications. Springer, New York, (2009).
[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).
[7] Stetkær, H.: Functional equations on groups. World Scientific, Publishing Co, Singapore, (2013).
[8] Stetkær, H.: Van Vleck’s functional equation for the sine. Aequationes Math. 90 (1), pp. 25-34, (2016).
[9] Stetkær, H.: Kannappan’s functional equation on semigroups with involution. Semigroup Forum. 94 (1), pp. 17-30, (2017).
[10] Van Vleck, E.B.: A functional equation for the sine. Ann. Math. 7, pp. 161-165, (1910).
Publicado
2018-09-25
Cómo citar
Fadli, B., Zeglami, D., & Kabbaj, S. (2018). An integral functional equation on groups under two measures. Proyecciones. Journal of Mathematics, 37(3), 565-581. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/3172
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