A generalization of Gajda's equation

Abstract

In the present paper we deal with a generalization of the classical Wilson's equation for mappings defined on a locally compact abelian group and taking their values in the field of complex numbers.

A note on a modification of Gajda’s equation

“…In Theorem 4 we proved that in the case of solutions of equation (4) function g is proportional to function f , which is additionally a solution of the d'Alembert functional equation (2). In Theorem 6 we obtained similar results for the solution of Eq.…”

“…It will be convenient to recall the general solution of (6) obtained in [2]. If the pair (g, f ) satisfies Eq.…”

On Gajda’s type quadratic equation on a locally compact abelian group

“…As another consequence of Theorem 2.5, we have the following result on the solution of the 1 functional equation there exists a quadratic function Q ∈ C(G) such that 7 f = 2Q * µ. 8 In the following corollary we solve the integral-functional equation (1.4), namely abelian groups. 13 Corollary 3.3.…”

“…(1.3) that is, according to our 7 knowledge, not in the literature. 8 Corollary 3.6. Let (G, +) be an abelian group, and choose arbitrarily elements α 1 , .…”

“…which was studied by Fechner and Székelyhidi in [8][9][10]. 12 Let µ ∈ M C (G) such that µ(G) :=  G dµ(t) = 1 2 .…”