Approximate functional inequalities by additive mappings

Abstract

Let n be a given positive integer, G an n-divisible abelian group, X a normed space and f : G → X. We prove a generalized Hyers-Ulam stabitity of the following functional inequality f (x) + f (y) + n f (z) n f x + y n + z + ϕ(x,y,z), ∀x,y,z ∈ G, which has been introduced in [3], under some conditions on ϕ : G × G × G → [0,∞) .

On functional inequalities associated with Drygas functional equation

“…The above-described effect: inequality implies equality was proved for some other functional equations. The interested reader can refer to [1], [2], [3], [4], [10], [11], [12], [14], [15], [16], [17], [18], [20] and [23] for a through account on the subject of functional inequalities.…”

Stability of cubic and quartic rho-functional inequalities in fuzzy normed spaces

“…M. Rassias' approach. 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 [4,10,12,13,17,23,24,25,27,28,29,30,31]). …”

On functional inequalities associated with Drygas functional equation

“…The interested reader can refer to [1], [2], [3], [4], [10], [11], [12], [14], [15], [16], [17], [18], [20] and [23] for a through account on the subject of functional inequalities.…”