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Recursive procedure in the stability of Fréchet polynomials. (English) Zbl 1343.39039
Summary: By means of a new stability result, established for symmetric and multi-additive mappings, and using the concepts of stability couple and of stability chain, we prove, by a recursive procedure, the generalized stability of two of Fréchet’s polynomial equations. We also give a new functional characterization of generalized polynomials and a new approach to solving the generalized stability of the monomial equation.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges 20M15 Mappings of semigroups 65Q30 Numerical aspects of recurrence relations
##### Keywords:
multi-additive mapping; Fréchet polynomial; monomial; stability
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