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Stability problem of Hyers-Ulam-Rassias for generalized forms of cubic functional equation

Authors:

Institution:

(1) Department of Mathematics Education, College of Education, Dankook University, Yongin, 448-701, Republic of Korea;(2) School of Mathematics, Korea Institute for Advanced Study, Seoul, 130-722, Republic of Korea

Abstract:

Let n ≥ 2 be an integer number. In this paper, we investigate the generalized Hyers-Ulam-Rassias stability in Banach spaces and also Banach modules over a Banach algebra and a C*-algebra and the stability using the alternative fixed point of an n-dimensional cubic functional equation in Banach spaces:

$f\left( {2\sum\limits_{j = 1}^{n - 1} {x_j + x_n } } \right) + f\left( {2\sum\limits_{j = 1}^{n - 1} {x_j - x_n } } \right) + 4\sum\limits_{j = 1}^{n - 1} {f(x_j ) = 16f} \left( {\sum\limits_{j = 1}^{n - 1} {x_j } } \right) + 2\sum\limits_{j = 1}^{n - 1} {(f(x_j + x_n ) + f(x_j - x_n ))} .$

Keywords:

Hyers-Ulam-Rassias stability cubic mapping

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