Geodesic
Stability of a generalization of the Fréchet functional equation
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 14 (2015) 
Malejki, Renata. Stability of a generalization of the Fréchet functional equation. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 14 (2015). http://geodesic.mathdoc.fr/item/AUPCM_2015_14_a6/
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     author = {Malejki, Renata},
     title = {Stability of a generalization of the {Fr\'echet} functional equation},
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     year = {2015},
     number = {14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPCM_2015_14_a6/}
}
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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 some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.