Superstability of Kannappan's and Van vleck's functional equations
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Authors
Belfakih Keltouma
- Faculty of Sciences, Department of Mathematics,, University Ibn Zohr, Agadir, Morocco.
Elqorachi Elhoucien
- Faculty of Sciences, Department of Mathematics,, University Ibn Zohr, Agadir, Morocco.
Themistocles M. Rassias
- Department of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, Greece.
Redouani Ahmed
- Faculty of Sciences, Department of Mathematics, University Ibn Zohr, Agadir, Morocco.
Abstract
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 \(S\).
Share and Cite
ISRP Style
Belfakih Keltouma, Elqorachi Elhoucien, Themistocles M. Rassias, Redouani Ahmed, Superstability of Kannappan's and Van vleck's functional equations, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 7, 894--915
AMA Style
Keltouma Belfakih, Elhoucien Elqorachi, Rassias Themistocles M., Ahmed Redouani, Superstability of Kannappan's and Van vleck's functional equations. J. Nonlinear Sci. Appl. (2018); 11(7):894--915
Chicago/Turabian Style
Keltouma, Belfakih, Elhoucien, Elqorachi, Rassias, Themistocles M., Ahmed, Redouani. "Superstability of Kannappan's and Van vleck's functional equations." Journal of Nonlinear Sciences and Applications, 11, no. 7 (2018): 894--915
Keywords
- Hyers-Ulam stability
- semigroup
- d'Alembert's equation
- automorpnism
- multiplicative function
MSC
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