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On the solutions of the linear integral equations of Volterra type
(Wiley, 2007) Odemir, Ismet; Temizer, O. Faruk
Some boundaries about the solution of the linear Volterra integral equations of the form f (t) = 1-K * f were obtained as vertical bar f (t)vertical bar <= 1, vertical bar f (t)vertical bar <= 2 and vertical bar f (t)vertical bar <= 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 vertical bar f (t)vertical bar <= 2(n) in (Integr Equ. Oper Theory 2002; 43:466-479), where t is an element of [0, infinity) 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 is an element of N) defined on the infinite interval [0, infinity) are given by our method, where f is the solution of the equation f (t) = 1 - K * f. Copyright (C) 2007 John Wiley & Sons, Ltd.