Fixed points and additive ρ-functional equations

초록

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.

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