Mittag-Leffler-Hyers-Ulam Stability For A First Order Delay Functional Differential Equation

In this paper, At first we define Mittag-Leffer-Hyers-Ulam and the Mittag-Leffer-Hyers-Ulam-Rassias stability and then by using the fixed point method, we prove the Mittag-Leffer-Hyers-Ulam and the Mittag-Leffer-Hyers-Ulam-Rassias stability for the first order delay differential equation of the form I can not transfer formulae here. Which F is a bounded continuous function and Τ is a fixed real number.For interval I, suppose that F is a continuous function such that satisfy the following conditionI can not transfer formulae here.Now suppose that the function F satisfy the following conditionI can not transfer formulae here.which Eq is Mittag-Leffler function. In this case there exists a unique function such that we have I can not transfer formulae here.for all... and ....In the other words, the function F is Mittag-Leffler-Hyers-Ulam stable. By changing in the conditions of F we can prove that the delay differential equation is Mittag-Leffler-Hyers-Ulam-Rassias stable.