FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

Abstract

In this paper, we solve the following (additive functional inequality

N(f(x + y) - f(x) - f(y), t) >= N(f(x + y/2) - 1/2 f(x) - f(y), t) (0.1)

and the following quadratic functional inequality

N(f (x + y) + f (x - y) - 2f (x) - 2f (y), t) (0.2)

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

in fuzzy normed spaces.

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