Abstract
We first examine the generalized Hyers-Ulam stability of functional inequality associated with module Jordan left derivation (resp., module Jordan derivation). Secondly, we study the functional inequality with linear Jordan left derivation (resp., linear Jordan derivation) mapping into the Jacobson radical.
Highlights
Introduction and PreliminariesLet A be an algebra over the real or complex field F and let M a left A-module resp., Abimodule
An additive mapping d : A→M is said to be a module left derivation resp., module derivation if d xy xd y yd x resp., d xy xd y d x y holds for all x, y ∈ A
The study of stability problems had been formulated by Ulam 1 during a talk in 1940: Under what condition does there exist a homomorphism near an approximate homomorphism? In the following year, Hyers 2 was answered affirmatively the question of Ulam for Banach spaces, which states that if ε > 0 and f : X→Y is a map with X a normed space, Y a Banach space such that
Summary
We first examine the generalized Hyers-Ulam stability of functional inequality associated with module Jordan left derivation resp., module Jordan derivation.
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