


Paper Title:
On Some Relations Among the Solutions of the Linear Volterra Integral Equations
Author(s):
Ismet Ozdemir and Faruk Temizer
Inönü Üniversitesi Eğitim Fakültesi,
44280Malatya,
Turkey
Abstract:
The sufficient conditions for y_{1}(x)≤ y_{2}(x) were given in [1] such that y_{m}(x)=f_{m}(x)+∫_{a}^{x} K_{m}(x, t)y_{m}(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 f(t)=1∫_{0}^{t}K(tτ)f(τ)dτ=1K*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)=1K* f and n≥ 2, it is derived that there exist the functions L_{2}, L_{3},..., L_{n} which can be obtained by means of K and some inequalities among the functions f, h_{2}, h_{3},..., h_{i} for i=2, 3,...., n are satisfied on the infinite interval [0, ∞), where h_{i} is the solution of the equation h_{i}(t)=1L_{i}* h_{i} and n is a natural number.
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