Abstract
We prove the generalized Hyers‐Ulam stability of the following functional inequalities:,, in the spirit of the Rassias stability approach for approximately homomorphisms.
Highlights
Introduction and preliminariesUlam [1] gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems
Among these was the following question concerning the stability of homomorphisms
Hyers [2] considered the case of approximately additive mappings f : E E1⁄4, where E and E1⁄4 are Banach spaces and f satisfies Hyers inequality f (x + y) f (x) f (y) for all x, y 3⁄4 E
Summary
Introduction and preliminariesUlam [1] gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. We prove the generalized Hyers-Ulam stability of the following functional inequalities: f (x) + f (y) + f (z) 2 Journal of Inequalities and Applications exists for all x 3⁄4 E and that L : E E1⁄4 is the unique additive mapping satisfying f (x) L(x) .
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