2019
Том 71
№ 8

# Gerus O. F.

Articles: 7
Article (Ukrainian)

### On hyperholomorphic functions of the space variable

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 459-465

For quaternionic-differentiable functions of a spatial variable, we prove a theorem on an integral over a closed surface. This theorem is an analog of the Cauchy theorem from complex analysis.

Brief Communications (Ukrainian)

### An estimate for the modulus of continuity of a quaternion singular Cauchy integral

Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1428–1435

We establish an upper bound for the modulus of continuity of a quaternion singular Cauchy integral in terms of the modulus of continuity of the integrand and a metric characteristic of a curve.

Article (Russian)

### Estimates for the modulus of a Cauchy-type integral and its derivatives

Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 732–743

In a domain bounded by a closed rectifiable Jordan curve, we obtain estimates for the modulus of a Cauchy-type integral and its derivatives in terms of the contour moduli of smoothness of the integrand and a metric characteristic of the curve.

Article (Russian)

### On the modulus of continuity of solid derivatives of a Cauchy-type integral

Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 476–484

We establish sufficient conditions for the existence of solid derivatives of a continuous extension of a Cauchy-type integral onto the closure of a domain and obtain an estimate for the moduli of continuity of these derivatives. We prove that the Newton-Leibniz formula is true for certain classes of Jordan rectifiable curves.

Article (Russian)

### Estimate of the modulus of continuity of a cauchy-type integral in a domain and on its boundary

Ukr. Mat. Zh. - 1996. - 48, № 10. - pp. 1321-1328

We estimate the modulus of continuity of a Cauchy-type integral in a closed domain and its limit values on the boundary in the case where the boundary of the domain is an arbitrary closed rectifiable Jordan curve.

Article (Ukrainian)

### Some estimates of smoothness moduli of Cauchy integrals

Ukr. Mat. Zh. - 1978. - 30, № 5. - pp. 594–601

Article (Ukrainian)

### Finite-dimensional smoothness of Cauchy-type integrals

Ukr. Mat. Zh. - 1977. - 29, № 5. - pp. 642–646