2019
Том 71
№ 6

# Mikhalin G. A.

Articles: 10
Article (Ukrainian)

### A generalization of the rogosinski-rogosinski theorem

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

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

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

Article (Ukrainian)

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

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

Article (Ukrainian)

### Kernel of the Voronoi means for a bounded sequence

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

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

Article (Ukrainian)

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

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

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

Article (Ukrainian)

### A theorem of Mazur-Orlicz type

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

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