## Stability and superstability of ring homomorphisms on non-archimedean Banach algebras.(English)Zbl 1216.39035

Summary: Using fixed point methods, we prove the superstability and generalized Hyers-Ulam stability of ring homomorphisms on non-Archimedean Banach algebras. Moreover, we investigate the superstability of ring homomorphisms in non-Archimedean Banach algebras associated with the Jensen functional equation.

### MSC:

 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges 46S10 Functional analysis over fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$ or the quaternions; non-Archimedean functional analysis
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