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Almahalebi, M.

On the stability of a generalization of Jensen functional equation. (English) Zbl 1399.39061

Acta Math. Hung. 154, No. 1, 187-198 (2018).
The author uses the fixed point method to prove the stability and the hyperstability of a generalization of Jensen functional equation \[ \sum_{k=0}^{n-1}f(x+b_ky)=nf(x) \] in the setting of Banach spaces. Here \(n \geq 2\), \(b_k=\exp(2i\pi k/n)\) for \(0\leq k \leq n-1\).
Reviewer: Mohammad Sal Moslehian (Mashhad)

Cited in 6 Documents

MSC:

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

Keywords:

stability; hyperstability; Jensen functional equation; fixed point method; Banach space
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References:

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