ADDITIVE rho-FUNCTIONAL EQUATIONS

作者：Park Choonkil; Jang Sun Young^*

来源：Journal of Computational Analysis and Applications, 2017, 22(6): 1035-1048.

• Hyers-Ulam stability
• additive rho-functional equation
• non-Archimedean normed space
• Banach space

In this paper, we solve the additive rho-functional equations
f(x + y) - f(x) - f(y) = rho(2f(x+y/2) - f(x) - f(y)), (0.1)
2f(x+y/2) - f(x) - f(y) = rho(f(x + y) - f(x) - f(y)) (0.2)
where rho is a fixed non-Archimedean number or a fixed real or complex number with rho not equal 1. Using the direct method, we prove the Hyers-Ulam stability of the additive rho-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces and in Banach spaces.

• 出版日期2017-6-1