ISSN : 1226-0657
In this paper, we solve the additive ρ-functional inequalities (0.1)<TEX>${\parallel}f(x+y)+f(x-y)-2f(x){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$</TEX>, where ρ is a fixed complex number with |ρ| < 1, and (0.2) <TEX>${\parallel}2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}f(x+y)+f(x-y)-2f(x){\parallel}$</TEX>, where ρ is a fixed complex number with |ρ| < 1. Furthermore, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces.
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