A fixed point approach to the Hyers-Ulam stability of an AQ functional equation on β-Banach modules

被引：0
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作者：
Tian Zhou Xu
John Michael Rassias
机构：
[1] Beijing Institute of Technology,School of Mathematics
[2] National and Capodistrian University of Athens,Pedagogical Department E.E., Section of Mathematics and Informatics
来源：
Journal of Inequalities and Applications | / 2012卷
关键词：
Hyers-Ulam stability; additive and quadratic equation; -Banach module; fixed point method;
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摘要：
In this paper, we establish the general solution and investigate the generalized Hyers-Ulam stability of the following mixed additive and quadratic functional equation: f(kx+ly)+f(kx−ly)=f(kx)+f(x)+12(k−1)[(k+2)f(x)+kf(−x)]+l2[f(y)+f(−y)] (k,l∈Z∖{0}) in β-Banach modules on a Banach algebra. In addition, we show that under some suitable conditions, an approximately mixed additive-quadratic function can be approximated by a mixed additive and quadratic mapping.
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