On uniform approximations to the solution of the Abel integral equation
type: Item
instance of: scholarly article
title: On uniform approximations to the solution of the Abel integral equation
zbMATH Open document ID: 1333.65144
DOI: 10.1134/S0965542515100139
author: G. V. Khromova
published in: Computational Mathematics and Mathematical Physics
publication date: 2016-01-13T00:00:00Z
review text: The author considers the Abel integral equation in the form \[ \int^x_0\frac{(x-t)^{\beta-1}} {\Gamma(\beta)}u(t)dt=f(x), \] where \(\Gamma\) is the gamma function, \(\beta \in (0,1)\), \(u\in C_{<0,1>}\) and \(f\) is defined by its approximation in \(L_{2}(0,1): \| f_{\delta}-f\|_{L_2}\leq\delta\). She uses the regularization method without restrictions on the parameter.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 6529522
zbMATH Keywords: Abel integral equation
zbMATH Keywords: uniform approximations
zbMATH Keywords: regularization methods
zbMATH Keywords: convergence
reviewed by: Josef Kofroň
MaRDI profile type: Publication
cites work: Theory of linear ill-posed problems and its applications. Transl., updated and revised from the Russian edition 1978
cites work: A method for constructing regularization techniques for equations of the first kind
cites work: On approximate solutions of the Abel equation
cites work: Q3671491
cites work: Q5528904
full work available at URL: s0965542515100139
OpenAlex ID: W2196193505
description: scientific article; zbMATH DE number 6529522