Published: 2017-08-05

Solutions and stability of generalized Kannappan’s and Van Vleck’s functional equations

Elhoucien Elqorachi , Ahmed Redouani

Abstract

We study the solutions of the integral Kannappan’s and Van Vleck’s functional equations
Sf(xyt)dμ(t) + ∫Sf(xσ(y)t)dμ(t) = 2f(x)f(y), x,y∈S;
Sf(xσ(y)t)dμ(t) - ∫Sf(xyt)dμ(t) = 2f(x)f(y), x,y∈S,
where S is a semigroup, is an involutive automorphism of S and μ is a linear combination of Dirac measures (δz_i)i∈I, such that for all i∈I, zi is in the center of S. We show that the solutions of these equations are closely related to the solutions of the d’Alembert’s classic functional equation with an involutive automorphism. Furthermore, we obtain the superstability theorems for these functional equations in the general case, where σ is an involutive morphism.

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Elqorachi, E., & Redouani, A. (2017). Solutions and stability of generalized Kannappan’s and Van Vleck’s functional equations. Annales Mathematicae Silesianae, 32, 169–200. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13919

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Domyślna okładka

Vol. 32 (2018)
Published: 2018-08-24


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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