HYERS-ULAM STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES

초록

In this paper, we introduce and solve the following additive (rho 1, rho 2) functional inequality (0.1) parallel to f (x + y + z) - f (x) - f(y) - f(z)parallel to <= parallel to rho 1 (f(x + z) - f(x) - f(z)parallel to + parallel to rho 2 (f(y + z) - f(y) - f(z))parallel to , where pi and rho 2 are fixed nonzero complex numbers with vertical bar rho 1 vertical bar+vertical bar rho 2 vertical bar < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (rho 1, rho 2) -functional inequality (0.1) in complex Banach spaces.

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