On the Bounds for the Derivatives of the Solutions of the Linear Volterra Integral Equations

Some bounds about the solution of the linear Volterra integral equations of the second type of the form with unit source term and positive monotonically increasing convolution kernel were obtained in [5, 6, 8-10]. The boundedness of functions f′; f″; ... ; f⁽ⁿ⁾; (n ∈ ℕ) defined on the infinite interval [0;1) were shown in [10, 12]. In this paper, it is shown that the results in [10, 12] for an equation in the same form can also be derived under different conditions than those of [10, 12].