Özdemir I.Temizer Ö.F.2024-08-042024-08-0420121449-5910https://hdl.handle.net/11616/91650The sufficient conditions for y1(x) ? y2(x) were given in [1] such that ym(x) = CMEX10.-1.integraltext fm(x) + ? x a Km(x, t)ym(t)dt, (m = 1, 2) and x ? [a, b]. Some properties such as positivity, boundedness and monotonicity of the solution of the linear Volterra integral equation of the form CMEX10.-1.integraltext t - f(t) = 1 - ? t 0 K(t - ?)f(?)d? = 1 - K f, (0 ? t < ?) were obtained, without solving this equation, in [3, 4, 5, 6]. Also, the boundaries for functions f', f'',.., f(n), (n ? N) defined on the infinite interval [0, ?) were found in [7, 8]. In this work, for the given equation f(t) = 1 - K * f and n ? 2, it is derived that there exist the functions L2, L3,.., Ln which can be obtained by means of K and some inequalities among the functions f, h2, h3,.., hi for i = 2, 3,.., n are satisfied on the infinite interval [0, ?), where hi is the solution of the equation hi(t) = 1 - Li * hi and n is a natural number. © 2012 Austral Internet Publishing.eninfo:eu-repo/semantics/closedAccessConvolution theoremEquivalence theoremLinear Volterra integral equations with convolution kernelArticle921232-s2.0-84869754205Q4