Stabilities in FDEs by Schauder's theorem

In a series of papers (Burton and Furumochi (Dyn. Syst. Appl. 10 (2001) 89-116; Funkcial. Ekvac. 44 (2001) 71-82; Nonlinear Anal. 49 (2002) 445-454; Dyn. Syst. Appl. 11 (2002) 499-521; Nonlinear Stud., to appear), Burton (Nonlinear Stud. 9 (2002) 181-190) Furumochi (Qualitative Theor. Differential Equations, to appear)), stability properties of solutions of FDEs have been investigated by means of fixed point theory. Here we obtain new stability results for super-linear FDEs by using Schauder's first theorem and a weighted norm, and show some examples.