Geodesic
Regularization of Abel Equation with the Use of Discontinuous Steklov Operator
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 599-603 
G. V. Khromova. Regularization of Abel Equation with the Use of Discontinuous Steklov Operator. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 599-603. http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a15/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For getting uniform approximations of the exact solution of Abel equation with an approximate right-hand part a simply constructed family of integral operators is suggested.

[1] Khromov A. P., Khromova G. V., “One modification of the Steklov operator”, Modern problems of function theory and their applications, Abstracts of the 15-th Saratov winter school, Saratov Univ. Press, Saratov, 2010, 181 (in Russian)

[2] Khromova G. V., “On a technique for constructing regularization methods for equations of the first kind”, Comput. Math. Math. Phys., 40:7 (2000), 955–960 | MR | Zbl

[3] Ivanov V. K., Vasin V. V., Tanana V. P., Theory of linear ill-posed problems and its applications, Nauka, M., 1978, 206 pp. (in Russian) | MR

[4] Ivanov V. K., “Fredholm integral equation of the first kind”, Differ. Equations, III:3 (1967), 410–421 (in Russian) | MR | Zbl

[5] Khromova G. V., “Error estimates of approximate solutions to equations of the first kind”, Doklady Math., 63:3 (2001), 390–394 | MR | MR | Zbl

[6] Khromova G. V., “On the approximate solutions of the Abel's equation”, Vestnik Moskovskogo universiteta. Ser. 15, 2001, no. 4, 5–9 (in Russian)