On the stability of unbounded differential equations in fuzzy k-normed spaces via fixed point method

First, using triangular norms and fuzzy sets, we define fuzzy k - normed spaces and then we study the stability of a class of differential equations. We apply a fixed point theorem to prove our stability results. Radu was the first mathematician who applied the fixed point method to prove the stability of functional equations both in normed spaces and random normed spaces. We consider the differential equation υ ʹ (ν ) = Г(ν, υ(ν)),which the related integral equation is υ (ν) = υ (m) - ∫_m^ν Г(τ, υ(τ)) dτ. In this article, by a fuzzy control function, we make stable the pseudo integral equation related to the differential equation. Next, we get an approximation for the pseudo integral equation by using the fixed point method. These results prove‎ Hyers - Ulam - Rassias stability and Hyers - Ulam stability in fuzzy k- normed spaces via fixed point method‎.