Stability of a mixed functional equation in several variables on Banach modules

作者：Najati Abbas^*; Rassias Themistocles M

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 72(3-4): 1755-1767.

DOI：10.1016/j.na.2009.09.017

• Generalized Hyers-Ulam stability
• Quadratic function
• Additive function
• Banach module
• Unital Banach algebra
• Generalized metric space
• Fixed point

In this piper, we establish the general solution of the functional equation
(n)Sigma(i=1)f(x(i) - 1/n (n)Sigma(j=1)x(j)) = (n)Sigma(i=1)f(x(i)) - nf(1/n (n)Sigma(i=1)x(i)) (n >= 2),
and use a fixed point method to prove its generalized Hyers-Ulam stability in Banach modules over a unital Banach algebra.

• 出版日期2010-2-1