Özet:
Some boundaries about the solution of the linear Volteira integral equations of the form f(t) = 1 -K * f were obtained as |f(r)|≤1, |f(t)|≤2 and |f(t)≤4 in (J. Math. Anal. Appl. 1978; 64:381-397; Int. J. Math. Math. Sci. 1982; 5(1): 123-131). The boundary of the solution function of an equation in this type was found as |f(t)|≤2n in (Integr. Equ. Oper. Theory 2002; 43:466-479), where t ∈ [0, ∈) and n is a natural number such that n≥2. In (Math. Comp. 2006; 75:1175-1199), it is shown that the boundary of the solution function of an equation in the same form can also be derived as that of (Integr. Equ. Oper. Theory 2002; 43:466-479) under different conditions than those of (Integr. Equ. Oper. Theory 2002; 43:466-479). In the present paper, the sufficient conditions for the boundedness of functions f, f′, f″,..., f(n+3), (n ∈ ℕ) defined on the infinite interval [0, ∞) are given by our method, where f is the solution of the equation f(t) = 1 - K * f. Copyright © 2007 John Wiley & Sons, Ltd.