ADDITIVE rho-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

Abstract

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

N (f (x+y)-f (x)-f (y), t) ˂= N (rho(2f (x +y)/2) - f (x)-f (y)), t) (0.1)

and

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

in fuzzy normed spaces, where rho is a fixed real number with vertical bar rho vertical bar ˂ 1.

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