2019
Том 71
№ 8

All Issues

Bondar A. V.

Articles: 14
Article (Ukrainian)

On differentiability of mappings of finite-dimensional domains into Banach spaces

Bondar A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 1. - pp. 3–11

The well-known Stepanov criterion of the differentiability (approximate differentiability) of real functions is generalized to mappings of subsets of $R^n$ n into Banach spaces satisfying the Rieffel sharpness condition, in particular, reflexive Banach spaces. For Banach spaces that do not satisfy the Rieffel sharpness condition, this criterion is not true.

Article (Ukrainian)

On differentiability of open mappings

Bondar A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1587–1600

The well-known Men’shov and Gehring-Lehto theorems on the differentiability of topological mappings of plane domains are generalized to the case of continuous open mappings of many-dimensional domains.

Article (Russian)

On differential properties of mappings into a Banach space

Bondar A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 500–509

We prove that the Rieffel sharpness condition for a Banach space E is necessary and sufficient for an arbitrary Lipschitz function f: [a, b]→E to be differentiable almost everywhere on a segment [a, b]. We establish that, in the case where the sharpness condition is not satisfied, the major part (in the category sense) of Lipschitz functions has no derivatives at any point of the segment [a, b].

Article (Ukrainian)

On local limit values of subharmonic and holomorphic functions

Bondar A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1312–1317

We prove theorems analogous to the local maximum principle and theorems on relation between limit sets, which can be used for studying singular sets.

Article (Ukrainian)

Pseudoanalyticity of continuous functions with the ?-preservation of angles

Bondar A. V., Lukyanova E. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1051–1057

Article (Ukrainian)

On pseudoanalyticity of continuous functions with constant ?-extension

Bondar A. V., Lukyanova E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 459–465

The theorem on pseudoanalyticity of continuous functions with constant ?-extension is proved; this is an analog of the well known results due to Bohr, Rademacher, Men'shov, and Trokhimchuk concerning the analyticity of functions with constant extension.

Article (Ukrainian)

Certain conditions for holomorphicity in Hilbert spaces

Bondar A. V., Romanenko V. Yu.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 1. - pp. 35–45

Article (Ukrainian)

Conditions for holomorphicity of Lipshitzian mappings of Hilbert spaces

Bondar A. V., Romanenko V. Yu.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 12. - pp. 1587–1592

Article (Ukrainian)

Derived operators and holomorphy conditions of Hilbert space mappings

Bondar A. V., Romanenko V. Yu.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 10. - pp. 1322–1327

Article (Ukrainian)

Continuous operator conformal mappings

Bondar A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 3. - pp. 314 - 322

Article (Ukrainian)

Differentiable operator-conformal mappings

Bondar A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 2. - pp. 160 - 168

Article (Ukrainian)

Multidimensional generalization of a theorem of D. E. Men'shov

Bondar A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1978. - 30, № 4. - pp. 435–443

Article (Ukrainian)

A generalization of the multidimensional Morera theorem

Bondar A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1978. - 30, № 3. - pp. 346–352

Article (Ukrainian)

The set of singular points of a univalent analytic function

Bondar A. V., Diab F. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1976. - 28, № 2. - pp. 147–158