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April, 2019 Exact Bounds and Approximating Solutions to the Fredholm Integral Equations of Chandrasekhar Type
Sheng-Ya Feng, Der-Chen Chang
Taiwanese J. Math. 23(2): 409-425 (April, 2019). DOI: 10.11650/tjm/181108

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.

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Sheng-Ya Feng. Der-Chen Chang. "Exact Bounds and Approximating Solutions to the Fredholm Integral Equations of Chandrasekhar Type." Taiwanese J. Math. 23 (2) 409 - 425, April, 2019. https://doi.org/10.11650/tjm/181108

Information

Received: 27 June 2018; Accepted: 14 November 2018; Published: April, 2019
First available in Project Euclid: 22 November 2018

zbMATH: 07055575
MathSciNet: MR3936006
Digital Object Identifier: 10.11650/tjm/181108

Subjects:
Primary: 45B05
Secondary: 26D15 , 47H10

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

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 2 • April, 2019
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