On some iterative numerical methods for a Volterra functional integral equation of the second kind

The problem of making resolution corrections in the scintillation spectrometry of continuous X rays is discussed. Analytical solutions are given to the integral equation which describes the effect of the statistical spread in pulse height. The practical necessity of making some kind of numerical analysis is pointed out. Difficulties with numerical methods arise from the fact that the observed pulse-height distribution cannot be defined precisely. As a result it is possible in practice only to find smooth "solutions". Additional difficulties arise if the numerical method is based on an invalid analytical procedure. For example matrix inversion is of doubtful value in making the resolution correction because there does not appear to be an inverse kernel for the integral equation in question.

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Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

International Journal of Analysis ◽

10.1155/2014/280709 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Mahmoud Bousselsal ◽

Sidi Hamidou Jah

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Existence Of Solutions ◽

Functional Integral ◽

Nonlinear Integral Equations ◽

Measure Of Weak Noncompactness ◽

Krasnoselskii’S Fixed Point Theorem ◽

Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

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On the existence of solutions of a set-valued functional integral equation of Volterra–Stieltjes type and some applications

Advances in Difference Equations ◽

10.1186/s13662-020-2531-4 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Ahmed Mohamed El-Sayed ◽

Shorouk Mahmoud Al-Issa

Keyword(s):

Integral Equation ◽

Existence Of Solutions ◽

Functional Integral ◽

Stieltjes Type

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Existence of Solutions for Functional Integral Equation Involving the Henstock-Kurzweil-Stieltjes Integral

Journal of Mathematics Research ◽

10.5539/jmr.v9n5p46 ◽

2017 ◽

Vol 9 (5) ◽

pp. 46

Author(s):

Hui Mei ◽

Guoju Ye ◽

Wei Liu ◽

Yanrong Chen

Keyword(s):

Integral Equation ◽

Fixed Points ◽

Measure Of Noncompactness ◽

Existence Of Solutions ◽

Functional Integral ◽

Stieltjes Integral

In this paper, we apply the method associated with the technique of measure of noncompactness and some generalizations of Darbo fixed points theorem to study the existence of solutions for a class of integral equation involving the Henstock-Kurzweil-Stieltjes integral. Meanwhile, an example is provided to illustrate our results.

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