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Accessible Unlicensed Requires Authentication Published by De Gruyter January 14, 2016

Hyers–Ulam stability of spherical functions

Belaid Bouikhalene and Elhoucien Eloqrachi

Abstract

In [15] we obtained the Hyers–Ulam stability of the functional equation

KGf(xtk·y)dμ(t)dk=f(x)g(y),x,yG,

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.

MSC: 39B52; 39B82

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Received: 2014-1-25
Accepted: 2015-1-20
Published Online: 2016-1-14
Published in Print: 2016-6-1

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