Geodesic
Approximation of Function and Its Derivative by the Modificated Steklov Operator
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 595-599.

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With the use of modification of Steklov operator are constructed families of integral operator which allow us to get uniform derivative on a closed. 
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A. A. Khromov. Approximation of Function and Its Derivative by the Modificated Steklov Operator. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 595-599. http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a14/

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

[2] 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)

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