Hyers-Ulam stability of functional equations with a square-symmetric operation

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Hyers-ulam stability of functional equations with a square-symmetric operation.

The stability of the functional equation f(x composite function y) = H(f(x), f(y)) (x, y in S) is investigated, where H is a homogeneous function and composite function is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.

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On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

The Hyers-Ulam stability problems of functional equations go back to 1940 when S. M. Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group see 1 . A partial answer was given by Hyers et al. 2, 3 under the assumption that the target space of the involved mappings is a Banach space. After the result of Hyers, Aoki 4 , and Bourgin 5, 6 dealt with this pro...

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Generalized Hyers–ulam Stability of Refined Quadratic Functional Equations

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ژورنال

عنوان ژورنال: Proceedings of the National Academy of Sciences

سال: 1998

ISSN: 0027-8424,1091-6490

DOI: 10.1073/pnas.95.22.12772