Abstract:
The convergence in the mean-square metric of the Lavrent'ev regularization method for an integral equation with involution is established. The proof of the convergence is based on studying the behavior of the resolvent of a certain integro-differential equation related to the original equation.
Keywords:
integral equation, regularization, involution, resolvent.
Citation:
A. P. Khromov, G. V. Khromova, “On the convergence of the Lavrent'ev method for an integral equation of the first kind with involution”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 1, 2012, 289–297; Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 88–97
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\by A.~P.~Khromov, G.~V.~Khromova
\paper On the convergence of the Lavrent'ev method for an integral equation of the first kind with involution
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 1
\pages 289--297
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 280
\issue , suppl. 1
\pages 88--97
\crossref{https://doi.org/10.1134/S0081543813020089}
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https://www.mathnet.ru/eng/timm798
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