<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Some bounds about the solution of the linear Volterra integral equations of the second type of the form <disp-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/fig5(p89).png"></inline-graphic></disp-formula> with unit source term and positive monotonically increasing convolution kernel were obtained in [5, 6, 8-10]. The boundedness of functions f′; f″; ... ; f<sup>(n)</sup>; (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].</p></abstract>

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].

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

Inönü Üniversitesi Egitim Fakültesi 44280-Malatya Turkey

Annals of West University of Timisoara - Mathematics and Computer Science

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...

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

Published Online: Jan 22, 2014

Page range: 89 - 113

DOI: https://doi.org/10.2478/awutm-2013-0018

Keywords
Linear Volterra integral equations with convolution kernel, Equivalence theorem, Convolution theorem

This content is open access.

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

Published Online: Jan 22, 2014

Page range: 89 - 113

DOI: https://doi.org/10.2478/awutm-2013-0018

KeywordsLinear Volterra integral equations with convolution kernel, Equivalence theorem, Convolution theorem

This content is open access.

Keywords
Linear Volterra integral equations with convolution kernel, Equivalence theorem, Convolution theorem