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Stability problem for Jensen-type functional equations of cubic mappings. (English) Zbl 1118.39013

The authors introduce the following Jensen type functional equations of cubic mappings between real linear spaces:

4f3x+y 4+4fx+3y 4=6fx+y 2+f(x)+f(y),9f2x+y 3+9fx+2y 3=16fx+y 2+f(x)+f(y)·

The general solution of both functional equations is f(x)=C(x)+Q(x)+A(x)+f(0), where C is cubic, Q is quadratic and A is additive, see K.-W. Jun and H.-M. Kim [Math. Inequal. Appl. 6, No. 2, 289–302 (2003; Zbl 1032.39015)]. The authors also prove the generalized Hyers-Ulam-Rassias stability of both equations.

MSC:
39B82Stability, separation, extension, and related topics
39B52Functional equations for functions with more general domains and/or ranges
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