On the stability of Jensen’s functional equation on groups

Abstract

In this paper we establish the stability of Jensen's functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and T (2, K), where K is an arbitrary commutative field with characteristic different from two. We also prove that any group A can be embedded into some group G such that the Jensen functional equation is stable on G.

On the E -Hyperstability of the Inhomogeneous σ -Jensen’s Functional Equation on Semigroups

“…Initially studied by Kominek [27], the stability problem of Jensen's functional equation has been explored by several mathematicians, including Jung [28], Faziev and Sahoo [29], Mihet [30], Ciepliński [31], and Almahalebi et al [32]. Various authors have studied the stability of the σ-Jensen functional equation ( 13) on abelian groups or vector spaces [33][34][35].…”

Stability of homomorphisms and derivations in $C^*$-ternary algebras

“…And then the stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem. (see [5], [7], [10], [13][14][15][16], [18][19][20][21][22], [28,29], [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] and [51]).…”

Ternary Derivations, Stability and Physical Aspects

“…[13,18,24,27,30,38] and references therein. Recently, the authors of [29] examined the stability of homomorphisms of ternary algebras by using the "direct method".…”