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We study a generalization of the Fréchet functional equation, stemming from a characterization of inner product spaces. We show, in particular, that under some weak additional assumptions each solution of… Click to show full abstract
We study a generalization of the Fréchet functional equation, stemming from a characterization of inner product spaces. We show, in particular, that under some weak additional assumptions each solution of such an equation is additive. We also obtain a theorem on the Ulam type stability of the equation. In its proof we use a fixed point result to show the existence of an exact solution of the equation that is close to a given approximate solution.
Keywords:
equation constant;
generalized chet;
functional equation;
equation;
stability;
chet functional
Journal Title: Aequationes mathematicae
Year Published: 2018
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Journal Title: Aequationes mathematicae
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!