JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, v. 18, NO. 3, Page. 569-586
Abstract
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)),
2f(x+y/2) - f(x) - f(y) = rho(f(x+y) - f(x) - f(y)),
where rho is a fixed non-Archimedean number or a fixed real or complex number with rho not equal 1. Using the fixed point method, we prove the Hyers-Ulam stability of the above additive rho-functional equations in non-Archimedean Banach spaces and in Banach spaces.