uniform approximations

On Operators with Discontinuous Range

Authors: Khromova G. V.

With the use of operators from approximation function theory we construct integral operators with discontinuous range of values, which make it possible to obtain uniform approximations of continuous functions on the whole interval of their definition. 

Approximation and Reconstruction of Continuous Function with Boundary Conditions

Authors: Shatalina O. I.

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.

Regularization of Abel Equation with the Use of Discontinuous Steklov Operator

Authors: Khromova G. V.

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.

Approximation of Function and Its Derivative by the Modificated Steklov Operator

Authors: Khromov A. A.

With the use of modification of Steklov operator are constructed families of integral operator which allow us to get uniform derivative on a closed.