2018
Том 70
№ 7

All Issues

Doronin V. G.

Articles: 6
Article (Russian)

Best mean square approximations by entire functions of finite degree on a straight line and exact values of mean widths of functional classes

Doronin V. G., Vakarchuk S. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1032–1043

We obtain exact Jackson-type inequalities in the case of the best mean square approximation by entire functions of finite degree $≤ σ$ on a straight line. For classes of functions defined via majorants of averaged smoothness characteristics $Ω_1(f, t ),\; t > 0$, we determine the exact values of the Kolmogorov mean ν-width, linear mean ν-width, and Bernstein mean $ν$-width, $ν > 0$.

Article (Russian)

Exact constants in Jackson-type inequalities for $L_2$-approximation on an axis

Doronin V. G., Ligun A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 92-98

We investigate exact constants in Jackson-type inequalities in the space $L_2$ for the approximation of functions on an axis by the subspace of entire functions of exponential type.

Article (Russian)

Exact constants in Jackson-type inequalities for $L_2$-approximation on an axis

Doronin V. G., Ligun A. A., Serdyuk A. S., Shydlich A. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 92-98

We investigate exact constants in Jackson-type inequalities in the space $L_2$ for the approximation of functions on an axis by the subspace of entire functions of exponential type.

Article (Russian)

On Jackson-Type Inequalities for Functions Defined on a Sphere

Babenko V. F., Doronin V. G., Ligun A. A., Shumeiko A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 3. - pp. 291–304

We obtain exact estimates of the approximation in the metrics $C$ and $L_2$ of functions, that are defined on a sphere, by means of linear methods of summation of the Fourier series in spherical harmonics in the case where differential and difference properties of functions are defined in the space $L_2$.

Article (Russian)

Exact constants in inequalities of the jackson type for quadrature formulas

Doronin V. G., Ligun A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 1. - pp. 46-51

We prove that if \(R_n \left( {f,\{ t_k \} ,\{ p_k \} } \right)\) is the error of a simple quadrature formula and ω(ε, δ)1 is the integral modulus of continuity, then, for any δ ≥/π andn,r = 1, 2, …, the following equality is true: \(\mathop {\inf }\limits_{\{ f_k \} ,\{ p_k \} } \mathop {\sup }\limits_{f \in L_1^r \backslash R_1 } \frac{{\left| {R_n (f,\{ t_k \} ,\{ p_k \} )} \right|}}{{\omega (f^{(r)} ,\delta )_1 }} = \frac{{\pi \left\| {D_1 } \right\|_\infty }}{{n^r }}\) whereD r is the Bernoulli kernel.

Article (Ukrainian)

Exact constant in the Jackson inequality in the space L2

Doronin V. G., Ligun A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1261–1265