2019
Том 71
№ 11

All Issues

Tomilov Yu. V.

Articles: 3
Article (Ukrainian)

Method of successive approximations for abstract volterra equations in a banach space

Mishura Yu. S., Tomilov Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 3. - pp. 376–382

We apply the method of successive approximations to abstract Volterra equations of the formx=f+a*Ax, whereA is a closed linear operator. The assumption is made that a kernela is continuous but is not necessarily of bounded variation.

Article (Russian)

On the asymptotic behavior of certain infinite-dimensional recurrence sequences

Tomilov Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 133-137

Under certain conditions imposed on an operator $B$, we obtain criteria of boundedness of sequences $x_{n+1} = A x_n + Bb_n,\; n > 0$, for any $x_0$ and bounded $\{b_n, \; n ≥ 0\}$ in infinite-dimensional spaces. The results are given in terms of spectral properties of the operator $A$.

Article (Russian)

On the asymptotic behavior of sequences given by recursion relations in a Banach space

Tomilov Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 5. - pp. 633–641

The criteria of boundedness and asymptotic periodicity are obtained for certain recursion sequences in a Banach space.