Ick-Soon Chang

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Let A be an algebra over the real or complex field F. An additive mapping d : A → A is said to be a left derivation resp., derivation if the functional equation d xy xd y yd x resp., d xy xd y d x y holds for all x, y ∈ A. Furthermore, if the functional equation d λx λd x is valid for all λ ∈ F and all x ∈ A, then d is a linear left derivation resp., linear(More)
We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central(More)
The functional inequality ‖f x 2f y 2f z ‖ ≤ ‖2f x/2 y z ‖ φ x, y, z x, y, z ∈ G is investigated, where G is a group divisible by 2, f : G→ X and φ : G3 → 0,∞ are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with 1 φ 2x,−x, 0 0 φ 0, x,−x x ∈ G and 2 limn→∞ 1/2 φ 2 1x, 2y, 2z 0, or limn→∞2φ(More)
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