Superstability problem for a large class of functional equations

Abstract

This paper treats superstability problem of the generalized Wilson's equationwhere G is an arbitrary locally compact group, that need not be abelian, K is a compact subgroup of G, ω K is the normalized Haar measure of K , is a finite group of K -invariant morphisms of G, μ is a complex measure with compact support and f, g : G −→ C are continuous complex-valued functions. We dont impose any condition on the continuous function f . In addition, superstability problem for a large class of related functional equations are considered.

A sine type functional equation on a topological group

“…for all x, y ∈ G. The first results of this kind have been established in [4] for the sine equation, in [2] for the exponential equation, in [3] for the cosine equation on an abelian group and in [11,16,17,18] for generalized Wilson's functional equations on any group.…”