Sal Moslehian, Themistocles M. Rassias
Abstract
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We prove the generalized Hyers-Ulam stability of the Cauchy functional equation f(x+y) = f(x)+f(y) and the quadratic functional equation f(x+ y) f(x - y) = 2f(x) + 2f(y) in non-Archimedean normed spaces.
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We prove the generalized Hyers-Ulam stability of the Cauchy functional equation f(x+y) = f(x)+f(y) and the quadratic functional equation f(x+ y) f(x - y) = 2f(x) + 2f(y) in non-Archimedean normed spaces.
Key concepts: Mathematics, Stability (learning theory), Pure mathematics, Functional equation, Functional analysis, Applied mathematics, Algebra over a field, Mathematical analysis