On the solutions of the linear integral equations of Volterra type

✍ Scribed by İsmet Özdemir; Ö. Faruk Temizer

• Publisher: John Wiley and Sons
• Year: 2007
• Tongue: English
• Weight: 307 KB
• Volume: 30
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.888

✦ Synopsis

Abstract

Some boundaries about the solution of the linear Volterra integral equations of the form f(t)=1−K*f were obtained as |f(t)|⩽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)|⩽2^n^ 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.