On the solutions of the linear integral equations of Volterra type
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.30, no.18, pp.2329-2369, 2007 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 30 Issue: 18
- Publication Date: 2007
- Doi Number: 10.1002/mma.888
- Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.2329-2369
- Inonu University Affiliated: Yes
Abstract
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.