On the stability of a class of cosine type functional equations

John Michael Rassias; Driss Zeglami; Ahmed Charifi

doi:10.5269/bspm.v37i2.29563

On the stability of a class of cosine type functional equations

John Michael Rassias National and Kapodistrian University of Athens Pedagogical Department of Education Mathematics and Informatics Section
Driss Zeglami ENSAM, Moulay Ismail University Department of Mathematics
Ahmed Charifi Ibn Tofail University Faculty Of Sciences Department of Mathematics

DOI: https://doi.org/10.5269/bspm.v37i2.29563

Keywords: stability, Superstability, D'Alembert equation, trigonometric functional equation

Abstract

The aim of this paper is to investigate the stability problem for the pexiderized trigonometric functional equation
f₁(xy)+f₂(xσ(y))=2g₁(x)g₂(y), x,y∈G,
where G is an arbitrary group, f₁,f₂,g₁ and g₂ are complex valued functions on G and σ is an involution of G. Results of this paper also can be extended to the setting of monoids (that is, a semigroup with identity) that need not be abelian.