ADDITIVE ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES.

In this paper, we solve the following additive p-functional inequalities N(f(x + y) - f(x) - f(y), t) ⩽ N (P ( 2f ( x + y / 2 ) - f(x) - f(y) ), t ) (0.1) and N ( 2f ( x + y / 2 ) - f(x) - f(y), t ) ⩽ N(p (f(x + y) - f(x) - f(y)) , t) (0.2) in fuzzy normed spaces, where p is a fixed real number with ∣p∣ < 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. [ABSTRACT FROM AUTHOR]