New criteria for global asymptotic stability of linear neutral differential equations by a fixed point approach

Abstract

New criteria ensuring global asymptotic stability of the zero solution
for a class of linear neutral differential equations in $C^{1}$ are proved, by using
two auxiliary functions on a contraction condition. Necessary and
sufficient conditions for the stability of our equation which also improves
recent results on this field are shown. Finally, an example is provided to illustrate
the feasibility and advantage of our results.