Geodesic
On the achievable level of accuracy in solving abstract ill-posed problems and nonlinear operator equations in Banach space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2022), pp. 21-27

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It is shown that for a wide class of ill-posed problems of finding the value of a discontinuous operator on an approximate element in Banach space, the level of accuracy of the resulting solution cannot exceed in order the error level of the input data. A similar result is established for a class of nonlinear operator equations with an approximate right-hand side. The classes of problems for which these orders coincide are specified.
Keywords: ill-posed problem, operator equation, error, accuracy estimate, Banach space. 
@article{IVM_2022_3_a2,
     author = {M. Yu. Kokurin and A. B. Bakushinsky},
     title = {On the achievable level of accuracy in solving abstract ill-posed problems and nonlinear operator equations in {Banach} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {21--27},
     publisher = {mathdoc},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_3_a2/}
}
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M. Yu. Kokurin; A. B. Bakushinsky. On the achievable level of accuracy in solving abstract ill-posed problems and nonlinear operator equations in Banach space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2022), pp. 21-27. http://geodesic.mathdoc.fr/item/IVM_2022_3_a2/