## 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
Full Text: