THE STABILITY OF ADDITIVE (α, β)-FUNCTIONAL EQUATIONS

초록

In this paper, we investigate the following (α, β)-functional equa-Abstract tions 2f(x) + 2f(z) = f(x − y) + α−1f(α(x + z)) + β−1f(β(y + z)), (0.1) 2f(x) + 2f(y) = f(x + y) + α−1f(α(x + z)) + β−1f(β(y − z)), (0.2) where α, β are fixed nonzero real numbers with α−1 + β−1 ≠ 3. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the (α, β)-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

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