Stability of a generalization of the Fréchet functional equation

Renata Malejki

Abstract


We prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces.  As the main tool we use a fixed point theorem for the function spaces. We end the paper with some new inequalities characterizing the inner product spaces.

Keywords


stability; hyperstability; characterization of inner product spaces; fixed point theorem; Fréchet equation

Mathematics Subject Classification (2010)


39B52; 39B82; 47H10

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