General criteria for hyperstability of Cauchy-type equations

Abstract

We provide three large classes of control functions that ensure the hyperstability of the Cauchy equation on restricted domains included in various types of commutative semigroups. Among other consequences, we obtain significant improvements on similar results known from the literature for several Aoki-Rassias-type control functions.

General hyperstability criteria for Jensen-type equations

“…The following Stolz-Cesàro-type criterion proved on normed linear spaces in Lemma 2.2 [7] will be useful further.…”

“…Solving techniques for a functional equation with composite solutions using its characteristic equation (the so-called section method) -have been described in [5]; several cases in which the stability or hyperstability of the characteristic equation is transmitted to the original equation are analyzed in [6]. A study similar to the present one, but made for Cauchy-type equations, was carried out in [7].…”