On an n-dimensional mixed type additive and quadratic functional equation

In this paper, we investigate the generalized Hyers–Ulam stability of the functional equation∑k2,…,kn=01fx1+∑i=2n(-1)kixi-2n-1f(x1)-2n-2∑i=2nf(xi)+f(-xi)=0for integer values of n such that n⩾2, where f is a function from a normed space X to a Banach space Y. The solutions of the equation are called...

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Bibliographic Details
Published in:Applied mathematics and computation 2014-02, Vol.228, p.13-16
Main Authors: Lee, Yang-Hi, Jung, Soon-Mo, Rassias, Michael Th
Format: Article
Language:English
Subjects:
Additives
Computation
Generalized Hyers–Ulam stability
Hyers–Ulam stability
Mathematical analysis
Mathematical models
Mixed type additive and quadratic function
Quadratic–additive mapping
Stability
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Summary:In this paper, we investigate the generalized Hyers–Ulam stability of the functional equation∑k2,…,kn=01fx1+∑i=2n(-1)kixi-2n-1f(x1)-2n-2∑i=2nf(xi)+f(-xi)=0for integer values of n such that n⩾2, where f is a function from a normed space X to a Banach space Y. The solutions of the equation are called additive–quadratic mappings.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.11.091