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Nonlinear stability of a quadratic functional equation with complex involution

Reza SaadatiGhadir Sadeghi — 2011

Archivum Mathematicum

Let X , Y be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping f : X Y satisfies f ( x + i y ) + f ( x - i y ) = 2 f ( x ) - 2 f ( y ) for all x , y X , then the mapping f : X Y satisfies f ( x + y ) + f ( x - y ) = 2 f ( x ) + 2 f ( y ) for all x , y X . Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method.

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