ON THE STABILITY OF ADDITIVE ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

Abstract

In this paper, we solve the following additive rho-functional inequalities

N (f(x + y) - f (x) - f(y) - rho (2f (x +y)/2 - f(x) - f(Y)),t) >= t/t + phi (x, y) (0.1)

and

N (2f (x + y/2) - f (x) - f (y) - rho (f (x + y) f (y)),t) >= t/t+phi(x, y) (0.2)

in fuzzy normed spaces, where rho is a fixed real number with rho not equal 1.

Using the direct method, we prove the Hyers-Ulam stability of the additive rho-functional inequalities (0.1) and (0.2) in fuzzy Banach spaces.