Using Banach Fixed Point Theorem To Study The Stability Of First-Order Delay Differential Equations

Abstract

In this paper we use the Banach fixed point theorem investigate the stability and asymptotic1 stability of the zero solution for the first order retarded delay differential equation=-∑_ j= ^N▒〖 b_j (t ,〖 3y〗 _t )3y(t)+f(t ,〖 3y〗 _t)〗 where the delay is constant. Also we give new conditions to ensure the stability and asymptotic stability of the zero solution of this equation.