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In  [15]  we obtained the Hyers–Ulam stability of the functional equation∫  K    ∫  G   f   (  x  t  k  ·  y  )d  μ   (  t  )d  k  =  f   (  x  )   g   (  y  )   ,    x  ,  y  ∈  G  ,    $ \int _{K}\int _{G} f(xtk\cdot y)\,d\mu (t)\,dk=f(x)g(y), \quad x, y\in G, $    where  G  is a Hausdorff locally compact topological group,  K  is a compact subgroup of morphisms of  G , μ 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.

Hyers–Ulam stability of spherical functions