2019
Том 71
№ 2

All Issues

Mikhalin G. A.

Articles: 10
Article (Ukrainian)

A generalization of the rogosinski-rogosinski theorem

Dekanov S. Ya., Mikhalin G. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 2. - pp. 220-227

We establish necessary and sufficient conditions for numerical functions αj(x), jN, xX, under which the conditions K(f j K(f 1) ∀j≥2 and \(\mathop {\lim }\limits_{U_r } \sum\nolimits_{j = 1}^\infty {\alpha _j (x)f_j (x) = a} \) yield \(\mathop {\lim }\limits_{U_r } f_1 (x) = a.\) The functions fj(x) are uniformly bounded on the set X and take values in a boundedly compact space L, and K(fj) is the kernel of the function fj. The well-known Rogosinski-Rogosinski theorem follows from the proved statements in the case where X = N, α j (x) ≡ αj, and the space L is the m-dimensional Euclidean space.

Article (Ukrainian)

Tauberian theorems with remainder for (H, p, α, β)-and (C, p, α, β)-methods of summation of functions of two variables

Aldanov V. M., Mikhalin G. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 8. - pp. 1036–1044

We consider a general method of obtaining Tauberian theorems with remainder for Hölder- and Cesarotype methods of summation.

Article (Ukrainian)

Tauberian theorems with remainder for summation methods of the Gel'fand and Cesaro type

Mikhalin G. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 7. - pp. 918-923

Article (Ukrainian)

Systems of Volterra nonlinear integral equations with unknown lower limit of integration

Mikhalin G. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 471-478

Article (Ukrainian)

Kernel of the Voronoi means for a bounded sequence

Davydov N. A., Mikhalin G. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 6. - pp. 675– 682

Article (Ukrainian)

Conditions for the kernel of a sequence to coincide with the kernels of its $(R,p_n,\alpha)$ and $(J,p_n)$ means

Mikhalin G. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 5. - pp. 504–509

Article (Ukrainian)

Theorems of Tauberian type for (J, pn) summation methods

Mikhalin G. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1977. - 29, № 6. - pp. 763–770

Article (Ukrainian)

A property of a class of (¯R, Pn,?) methods for summation of series and Tauberian theorems

Mikhalin G. A., Teslenko L. S.

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Ukr. Mat. Zh. - 1977. - 29, № 2. - pp. 194–203

Article (Ukrainian)

A theorem of Mazur-Orlicz type

Mikhalin G. A.

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Ukr. Mat. Zh. - 1974. - 26, № 4. - pp. 460–468

Article (Ukrainian)

A generalization of a theorem of agnew and the equivalence of kozhim methods to cesaro methods of summation of series on the set of bounded sequences

Mikhalin G. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1974. - 26, № 1. - pp. 95–98