Abstract
In this note we investigate the generalized Hyers–Ulam–Rassias stability for the new cubic type functional equation f ( x + y + 2 z ) + f ( x + y − 2 z ) + f ( 2 x ) + f ( 2 y ) = 2 [ f ( x + y ) + 2 f ( x + z ) + 2 f ( x − z ) + 2 f ( y + z ) + 2 f ( y − z ) ] by using the fixed point alternative. The first systematic study of fixed point theorems in nonlinear analysis is due to G. Isac and Th.M. Rassias [Internat. J. Math. Math. Sci. 19 (1996) 219–228].
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