Approximation and Reconstruction of Continuous Function with Boundary Conditions

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.