Abstract
In this paper, we prove the Hyers-Ulam stability of the following function inequalities: in Banach spaces.MSC:39B62, 39B52, 46B25.
Highlights
Introduction and preliminariesThe stability problem of functional equations originated from the question of Ulam [ ] in concerning the stability of group homomorphisms
In this paper, we prove the Hyers-Ulam stability of the following function inequalities: f (x) + f (y) + f (z) ≤ Kf x + y + z K
1 Introduction and preliminaries The stability problem of functional equations originated from the question of Ulam [ ] in concerning the stability of group homomorphisms
Summary
The mapping A : X → Y is additive. Assume that T : X → Y is another additive mapping satisfying Let f : X → Y be a mapping satisfying f (x) + f (y) + f (z) ≤ Kf x + y + z + θ x p + y p + z p K for all x, y, z ∈ X. There exists a unique additive mapping A : X → Y such that f (x) – A(x). Let f : X → Y be a mapping such that f (x) + f (y) + Kf (z) ≤ Kf x+y +z (K + )f ( ) ≤ Kf ( ).
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