Superstability of Kannappan's and Van vleck's functional equations

Keltouma, Belfakih ¹ ; Elhoucien, Elqorachi ¹ ; Rassias, Themistocles M. ² ; Ahmed, Redouani ³

¹ Faculty of Sciences, Department of Mathematics,, University Ibn Zohr, Agadir, Morocco
² Department of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, Greece
³ Faculty of Sciences, Department of Mathematics, University Ibn Zohr, Agadir, Morocco

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 7, p. 894-915.

Résumé

In this paper, we prove the superstability theorems of the functional equations

$\mu(y)f(x\sigma(y)z_0)\pm f(xyz_0) =2f(x)f(y), \;x,y\in S,\quad \mu(y)f( \sigma(y)xz_0)\pm f(xyz_0) = 2f(x)f(y), \;x,y\in S,$

where $S$ is a semigroup, $\sigma$ is an involutive morphism of $S$, and $\mu:$ $S\longrightarrow \mathbb{C}$ is a bounded multiplicative function such that $\mu(x\sigma(x))=1$ for all $x \in S$, and $z_{0}$ is in the center of $S$.

Détail

DOI : 10.22436/jnsa.011.07.03

Classification : 39B32, 39B82
Keywords: Hyers-Ulam stability, semigroup, d'Alembert's equation, automorpnism, multiplicative function

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