Additive ρ-functional inequalities
نویسندگان
چکیده
In this paper, we solve the additive ρ-functional inequalities ‖f(x+ y)− f(x)− f(y)‖ ≤ ∥∥∥∥ρ(2f (x+ y 2 ) − f(x)− f(y) )∥∥∥∥ , (1) ∥∥∥∥2f (x+ y 2 ) − f(x)− f(y) ∥∥∥∥ ≤ ‖ρ (f(x+ y)− f(x)− f(y))‖ , (2) where ρ is a fixed non-Archimedean number with |ρ| < 1 or ρ is a fixed complex number with |ρ| < 1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (1) and (2) in non-Archimedean Banach spaces and in complex Banach spaces, and prove the Hyers-Ulam stability of additive ρ-functional equations associated with the additive ρ-functional inequalities (1) and (2) in non-Archimedean Banach spaces and in complex Banach spaces. c ©2014 All rights reserved.
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Additive Ρ –functional Inequalities in Non–archimedean Normed Spaces
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