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On stability of the functional equation of \(p\)-Wright affine functions in \((2,\alpha)\)-Banach spaces. (English) Zbl 1425.39014

Summary: Stability of functional equations has recent applications in many fields. We show that the stability results obtained by J. Brzdęk [Aequationes Math. 85, No. 3, 497–503 (2013; Zbl 1272.39015)] and concerning the functional equation of the \(p\)-Wright affine function: \[ f(px_1+(1- p)x_2)+f((1- p)x_1+px_2)=f(x_1)+f(x_2), \] can be proved also in \((2,\alpha)\)-Banach spaces, for some real number \(\alpha\in (0,1)\). This is done using some fixed-point theorem.

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
39B82 Stability, separation, extension, and related topics for functional equations
47H10 Fixed-point theorems

Citations:

Zbl 1272.39015
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