2019
Том 71
№ 8

All Issues

Bezkryla S. I.

Articles: 2
Article (Ukrainian)

On one inequality for the moduli of continuity of fractional order generated by semigroups of operators

Bezkryla S. I., Chaikovs'kyi A. V., Nesterenko A. N.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 3. - pp. 310-324

A new inequality for the moduli of continuity of fractional order generated by semigroups of operators is obtained. This inequality implies a generalization of the well-known statement that there exists an $α$-majorant, which is not a modulus of continuity of order $α$ generated by a semigroup of operators, to the case of noninteger values of $α$.

Brief Communications (Ukrainian)

On the Third Moduli of Continuity

Bezkryla S. I., Chaikovs'kyi A. V., Nesterenko A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1420-1424

An inequality for the third uniform moduli of continuity is proved. This inequality implies that an arbitrary 3-majorant is not necessarily a modulus of continuity of order 3.