2019
Том 71
№ 10

# Bondar A. V.

Articles: 15
Article (Ukrainian)

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

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

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

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 (Russian)

### On local limit values of subharmonic and holomorphic functions

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 (Russian)

### Pseudoanalyticity of continuous functions with the ?-preservation of angles

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

The following theorem is proved: Every continuous function satisfying the condition $K'_{\sigma}$ is pseudo-analytic. The condition $K'_{\sigma}$ is a generalization of the Men'shov condition, well known in the theory of analytic functions.

Article (Russian)

### On pseudoanalyticity of continuous functions with constant $σ$-extension

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

The theorem on pseudoanalyticity of continuous functions with constant $σ$-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 (Russian)

### On the structure of sets of $σ$-monogeneity for continuous functions

Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 226–232

The notion of the sets of σ-monogeneity for continuous functions is introduced which makes it possible to study pseudo-analytic properties of these functions. The theorem on the structure of these sets is proved.

Article (Ukrainian)

### Certain conditions for holomorphicity in Hilbert spaces

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

Article (Ukrainian)

### Conditions for holomorphicity of Lipshitzian mappings of Hilbert spaces

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

Article (Ukrainian)

### Derived operators and holomorphy conditions of Hilbert space mappings

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

Article (Ukrainian)

### Continuous operator conformal mappings

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

Article (Ukrainian)

### Differentiable operator-conformal mappings

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

Article (Ukrainian)

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

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

Article (Ukrainian)

### A generalization of the multidimensional Morera theorem

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

Article (Ukrainian)

### The set of singular points of a univalent analytic function

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