QUADRATIC ρ-FUNCTIONAL EQUATIONS

초록

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

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