Hyers-Ulam stability of the spherical functions

Abstract

In \cite{bbb} the authors obtained the Hyers-Ulam stability of the functional equation $$ \int_{K}\int_{G} f(xtk\cdot y)d\mu(t)dk=f(x)g(y), \; x, y \in G ,$$ where $G$ is a Hausdorff locally compact topological group, $K$ is a copmact subgroup of morphisms of $G$, $\mu$ is a $K$-invariant complex measure with compact support, provided that the continuous function $f$ satisfies some Kannappan Type condition. The purpose of this paper is to remove this restriction.