On a Method of Proving the Hyers-Ulam Stability of Functional Equations on Restricted Domains (original) (raw)
We show that generalizations of some (classical) results on the Hyers-Ulam stabil- ity of functional equations, in several variables, can be very easily derived from a simple result on stability of a functional equation in single variable.
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Some Further Generalizations of the Hyers–Ulam–Rassias Stability of Functional Equations
Journal of Mathematical Analysis and Applications, 2001
In this paper we study the Hyers–Ulam–Rassias stability theory by considering the cases where the approximate remainder φ is defined bywhere (G, ∗ ) is a certain kind of algebraic system, E is a real or complex Hausdorff topological vector space, and f, g, h are mappings from G into E. We prove theorems for the Hyers–Ulam–Rassias stability of the above three kinds of functional equations and obtain the corresponding error formulas.
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