Gerus O. F.
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.
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.
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.
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.
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.
Ukr. Mat. Zh. - 1978. - 30, № 5. - pp. 594–601
Ukr. Mat. Zh. - 1977. - 29, № 5. - pp. 642–646