Abstract
Let G be a commutative semigroup, or ℂ and . Generalizing the stability of the functional equation with bounded difference (Najdecki in J. Inequal. Appl. 2007:79816, 2007), we prove the stability of the above functional equation with unbounded differences. We also give a more precise description for bounded components of . MSC:39B82.
Highlights
Appl. 2007:79816, 2007), we prove the stability of the above functional equation with unbounded differences
We investigate bounded functions satisfying each of ( . ) and ( . )
Let f : G → K be a bounded function satisfying
Summary
For all x, y ∈ G with any norm · in Kn. there exist ideals I, J ⊂ Kn such that Kn = I ⊕ J, PF is bounded and QF satisfies In this paper, generalizing the above result we consider the functional inequalities There exist ideals I, J ⊂ Kn such that Kn = I ⊕ J, PF is bounded and QF satisfies
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