Taiwanese Journal of Mathematics

Exact Bounds and Approximating Solutions to the Fredholm Integral Equations of Chandrasekhar Type

Sheng-Ya Feng and Der-Chen Chang

Full-text: Open access

Abstract

In this paper, we study the $L^p$ solutions of the Fredholm integral equations with Chandrasekhar kernels. The Hilbert type inequality is resorted to establish an existence and uniqueness result for the Fredholm integral equation associated with Chandrasekhar kernel. A couple of examples well support the condition and extend the classical results in the literature with one generalizing the classical Chandrasekhar kernel. In order to approximate the original solution, a truncated operator is introduced to overcome the non-compactness of the integral operator. An error estimate of the convergence is made in terms of the truncated parameter, the upper bounds of the symbolic function constituting the integral kernel and initial data to the equation.

Article information

Source
Taiwanese J. Math., Volume 23, Number 2 (2019), 409-425.

Dates
Received: 27 June 2018
Accepted: 14 November 2018
First available in Project Euclid: 22 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1542855640

Digital Object Identifier
doi:10.11650/tjm/181108

Mathematical Reviews number (MathSciNet)
MR3936006

Subjects
Primary: 45B05: Fredholm integral equations
Secondary: 26D15: Inequalities for sums, series and integrals 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
Chandrasekhar kernel Hilbert-type inequality Fredholm integral equation $L^p$ norm approximating solution

Citation

Feng, Sheng-Ya; Chang, Der-Chen. Exact Bounds and Approximating Solutions to the Fredholm Integral Equations of Chandrasekhar Type. Taiwanese J. Math. 23 (2019), no. 2, 409--425. doi:10.11650/tjm/181108. https://projecteuclid.org/euclid.twjm/1542855640


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