On the Normal Stability of Functional Equations

Abstract

Abstract. In the paper two types of stability and of b-stability of functional equations are distinguished.

Stability has many names

“…2. Normal stability implies uniform b-stability and the normal uniform b-stability implies normal stability but not conversely [17].…”

“…It is also stable since for every ε > 0 every positive number δ < 1 is "good" for the stability. This stability is not normal since normal stability implies b-stability [17].…”

“…Equation (6) in the class of continuous functions from IxR to I is (see [16]) -stable (normally, strongly) only for I=R, -b-stable (normally, strongly), uniformly b-stable and restrictedly uniformly b-stable (normally) only for I being bounded or I=R, -inversely b-stable, absolutely b-stable, inversely uniformly b-stable, absolutely uniformly b-stable, superstable, uniformly superstable and inversely superstable only for I bounded, -inversely stable, absolutely stable and hyperstable for no I, -inversely hyperstable for every I. Equation (7) in the class of continuous functions from IxR to I is (see [16] and [17] Remark. The stability of Eq.…”

Generalized Hyers-Ulam Stability of the Pexider Functional Equation

“…was investigated by Lee and Jun [5] (see also [6][7][8][9]). Now, for given mappings f , g, h : V × V → Y, we consider the Pexider functional equation…”