Stability and hyperstability of a quadratic functional equation and a characterization of inner product spaces

We have proved theHyers-Ulam stability and the hyperstability of the quadratic functional equation f (x + y + z) + f (x + y − z) + f (x − y + z) + f (−x + y + z) = 4[f (x) + f (y) + f (z)] in the class of functions from an abelian group G into a Banach space.

Bibliographic Details
Main Authors: Kim Gwang Hui, El-Fassi Iz-iddine, Park Choonkil
Format: Article
Language:English
Published: De Gruyter 2018-11-01
Series:Demonstratio Mathematica
Subjects:
Online Access:http://www.degruyter.com/view/j/dema.2018.51.issue-1/dema-2018-0027/dema-2018-0027.xml?format=INT
Description
Summary:We have proved theHyers-Ulam stability and the hyperstability of the quadratic functional equation f (x + y + z) + f (x + y − z) + f (x − y + z) + f (−x + y + z) = 4[f (x) + f (y) + f (z)] in the class of functions from an abelian group G into a Banach space.
ISSN:2391-4661