A sine type functional equation on a topological group.

  • D. Zeglami Moulay Ismail University.
  • S. Kabbaj Ibn Tofail University.
  • M. Tial Ibn Tofail University.

Resumen

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.

Biografía del autor

D. Zeglami, Moulay Ismail University.
Department of Mathematics, ENSAM.
S. Kabbaj, Ibn Tofail University.
Department of Mathematics, Faculty of Sciences.
M. Tial, Ibn Tofail University.
Department of Mathematics, Faculty of Sciences.

Citas

J. Aczél, J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, New York, (1989).

J. A. Baker, J. Lawrence, and F. Zorzitto, The stability of the equation f(x + y) = f(x)f(y), Proc. Amer. Math. Soc. 74, pp. 242-246, (1979).

J. A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 , pp. 411-416, (1980).

P. W. Cholewa, The stability of the sine equation, Proc. Amer. Math. Soc. 88, No. 4, pp. 631-634, (1983).

J. Chung and D. Kim, Sine functional equation in several variables, Archiv der Mathematik 86, No 5, pp. 425-429, (2006).

I. Corovei, The sine functional equation on 2-divisible groups, Mathematica 47, No 1, pp. 49-52, (2005).

Pl. Kannappan, On sine functional equation, Studia Sci. Math. Hung., 4, pp. 331-333, (1969).

Pl. Kannappan, Functional Equations and Inequalities with Applications. Springer Monographs in Mathematics. Springer, New York, xxiv+810, (2009).

G. H. Kim, A stability of the generalized sine functional equations, J. Math. Anal. Appl., 331, pp. 886-894, (2007).

S. Kurepa, On the functional equation f(x+y)f(x−y) = f(x)2−f(y)2, Ann. Polon. Math., 10 , pp. 1-5, (1961).

A. Roukbi, D. Zeglami and S. Kabbaj, Hyers-Ulam stability of Wilson’s functional equation, J. Math. Sci. Adv. Appl., 22, pp. 19-26, (2013).

P. Sinopoulos, Generalized sine equations, I, Aequationes math., 48, No. 2, pp. 171-193, (1994).

H. Stetkær, Functional equations on groups, World Scientific Publishing, Hackensack, xvi+378, (2013).

H. Stetkær, Van Vleck’s functional equation for the sine. Aequationes Math. 90 (1), pp. 25—34, (2016).

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

D. Zeglami, B. Fadli, S. Kabbaj, On a variant of µ-Wilson’s functional equation on a locally compact group, Aequationes Math., 89, pp. 1265-1280, (2015).

D. Zeglami, A. Charifi and S. Kabbaj, Superstability problem for a large class of functional equations, Afr. Mat., 27, pp. 469-484, (2016).

D. Zeglami, M. Tial and B. Fadli, Wilson’s Type Hilbert-space valued functional equations, Adv. Pure. Appl. Math., 7, No. 3, pp. 189-196, (2016).

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

D. Zeglami, M. Tial, S. Kabbaj, The integral sine addition law, Submited to Proyecciones J. of Math.

Publicado
2019-05-29
Cómo citar
[1]
D. Zeglami, S. Kabbaj, y M. Tial, «A sine type functional equation on a topological group»., PJM, vol. 38, n.º 2, pp. 221-235, may 2019.
Sección
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