Geodesic
Approximation and Reconstruction of Continuous Function with Boundary Conditions
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 603-608

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This work deals with a family of integral operators, which are used to get uniform approximations to continuous function with boundary conditions (stated approximations with the same conditions as well); the Kolmogorov–Nikolsky problem is solved on some compact class. Acquired problem from the theory of ill-posed problems (so-called problem of reconstruction of a continuous function using its mean-root-square approximation) is solved via the goal family of integral operators as well. 
@article{ISU_2014_14_4_a16,
     author = {O. I. Shatalina},
     title = {Approximation and {Reconstruction} of {Continuous} {Function} with {Boundary} {Conditions}},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {603--608},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a16/}
}
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O. I. Shatalina. Approximation and Reconstruction of Continuous Function with Boundary Conditions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 603-608. http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a16/