Hyers-Ulam stability; additive rho-functional equation; non-Archimedean normed space; Banach space
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, v. 22, no. 6, page. 1035-1048
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.