A variant of the quadratic functional equation on semigroups

B. Fadli, D. Zeglami, S. Kabbaj

Resumen


Let S be a semigroup, let H be an abelian group which is uniquely 2-divisible, and let σ be an involutive automorphism of S. We express the solutions f : SH of the following variant of the quadratic functional equation

f(xy) + f(σ(y)x) = 2f(x) + 2f(y), x, yS,

in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation.


Palabras clave


Symmetrized additive Cauchy equation ; Quadratic equation ; Additive function ; Semigroup

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Referencias


H. Drygas, Quasi-inner products and their applications, in: Advances in Multivariate Statistical Analysis (ed. A. K. Gupta), D. Reidel Publishing Co., pp. 13-30, (1987).

B. Fadli, D. Zeglami and S. Kabbaj, On a Gajda’s type quadratic equation on a locally compact abelian group, Indagationes Math. 26 (4), pp. 660-668, (2015).

B. Fadli, D. Zeglami and S. Kabbaj, A variant of Wilson’s functional equation, Publ. Math. Debrecen 87 (3-4), pp. 415-427, (2015).

B. Fadli, D. Zeglami and S. Kabbaj, A variant of Jensen’s functional equation on semigroups, Demonstratio Math. 49 (4), pp. 413-420, (2016).

B. Fadli, A. Chahbi, Iz. EL-Fassi and S. Kabbaj, On Jensen’s and the quadratic functional equations with involutions, Proyecciones (Antofagasta) 35 (2), pp. 213-223, (2016).

V. A. Faĭziev and P. K. Sahoo, Solution of Whitehead equation on groups, Math. Bohem. 138(2), pp. 171-180, (2013).

PL. Kannappan, Functional equations and inequalities with applications, Springer, New York, (2009).

C.T. Ng, Jensen’s functional equation on groups, III, Aequationes Math. 62 (1-2), pp. 143-159, (2001).

P. de Place Friis and H. Stetkær, On the quadratic functional equation on groups, Publ. Math. Debrecen 69 (1-2), pp. 65-93, (2006).

P. Sinopoulos, Functional equations on semigroups, Aequationes Math. 59(3), pp. 255-261, (2000).

H. Stetkær, Functional equations on abelian groups with involution, Aequationes Math. 54 (1-2), pp. 144-172, (1997).

H. Stetkær, On a variant of Wilson’s functional equation on groups, Aequationes Math. 68 (3), pp. 160-176, (2004).

H. Stetkær, Functional Equations on Groups, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, (2013).

H. Stetkær, A variant of d’Alembert’s functional equation, Aequationes Math. 89 (3), pp. 657-662, (2015).

H. Stetkær, The kernel of the second order Cauchy difference on semi-groups, Aequationes Math. (2016). DOI 10.1007/s00010-016-0453-8.

D. Zeglami, B. Fadli and S. Kabbaj, On a variant of μ-Wilson’s functional equation on a locally compact group, Aequationes Math. 89 (5), pp. 1265-1280, (2015).


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