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A fixed points approach to stability of the Pexider equation. (English) Zbl 1307.39016

Summary: Using the fixed point theorem we establish the Hyers-Ulam-Rassias stability of the generalized Pexider functional equation \[ \frac{1}{|K|}\sum_{k\in K}f(x+k\cdot y)=g(x)+h(y), \quad x, y \in E, \] from a normed space \(E\) into a complete \(\beta\)-normed space \(F\), where \(K\) is a finite abelian subgroup of the automorphism group of the group \((E, +)\).

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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