Izvestiya Mathematics, ISSN 1064-5632, 2016, Volume 80, Issue 2, pp. 165 - 184

We study properties of sets for which there is a continuous selection from the set of almost-best approximants. We establish relations between local and global...

Moduli of approximative continuity | B-approximative infinite connectedness | ϵ-selection | Monotone path-connected sets | δ-solarity | B-infinite connectedness | MATHEMATICS | moduli of approximative continuity | monotone path-connected sets | APPROXIMATION | OPERATOR | BANACH-SPACES | delta-solarity | SETS | epsilon-selection | SPLINES

Moduli of approximative continuity | B-approximative infinite connectedness | ϵ-selection | Monotone path-connected sets | δ-solarity | B-infinite connectedness | MATHEMATICS | moduli of approximative continuity | monotone path-connected sets | APPROXIMATION | OPERATOR | BANACH-SPACES | delta-solarity | SETS | epsilon-selection | SPLINES

Journal Article

Izvestiya Mathematics, ISSN 1064-5632, 2018, Volume 82, Issue 4, pp. 837 - 859

We study conditions on sets in asymmetric spaces under which there are continuous epsilon-selections or continuous selections for the metric projection. In...

asymmetric spaces | polyhedral spaces | metric projection | continuous ϵ-selection | MATHEMATICS | continuous epsilon-selection | SETS

asymmetric spaces | polyhedral spaces | metric projection | continuous ϵ-selection | MATHEMATICS | continuous epsilon-selection | SETS

Journal Article

Mathematical Notes, ISSN 0001-4346, 11/2018, Volume 104, Issue 5, pp. 727 - 734

We study sets admitting a continuous selection of near-best approximations and characterize those sets in Banach spaces for which there exists a continuous...

continuous ε-selection | Mathematics, general | Mathematics | fixed point | MATHEMATICS | continuous epsilon-selection | SETS

continuous ε-selection | Mathematics, general | Mathematics | fixed point | MATHEMATICS | continuous epsilon-selection | SETS

Journal Article

Izvestiya Mathematics, ISSN 1064-5632, 2017, Volume 81, Issue 3, pp. 645 - 669

We study properties of set-valued mappings F admitting a continuous selection f which is a continuous epsilon-selection (from the set of epsilon-closest...

Continuous selection for set-valued mappings | B-neighbourhood infinite connectedness | B-approximative infinite connectedness | ϵ-selection | B-infinite connectedness | Fixed-point theorems | MATHEMATICS | (B)over-circle-infinite connectedness | (B)over-circle-approximative infinite connectedness | EXTREMAL PROBLEMS | (B)over-circle-neighbourhood infinite connectedness | epsilon-selection | fixed-point theorems | continuous selection for set-valued mappings

Continuous selection for set-valued mappings | B-neighbourhood infinite connectedness | B-approximative infinite connectedness | ϵ-selection | B-infinite connectedness | Fixed-point theorems | MATHEMATICS | (B)over-circle-infinite connectedness | (B)over-circle-approximative infinite connectedness | EXTREMAL PROBLEMS | (B)over-circle-neighbourhood infinite connectedness | epsilon-selection | fixed-point theorems | continuous selection for set-valued mappings

Journal Article

Mathematical Notes, ISSN 0001-4346, 4/2011, Volume 89, Issue 3, pp. 572 - 576

Sets in which some convex subsets admit local (global) continuous ɛ-selections are studied. In particular, it is shown that if, for any number ɛ > 0, some...

convex set | approximatively compact set | δ-sun | Mathematics, general | acyclic upper semicontinuous ε-selection | Mathematics | Banach space | MATHEMATICS | acyclic upper semicontinuous epsilon-selection | delta-sun

convex set | approximatively compact set | δ-sun | Mathematics, general | acyclic upper semicontinuous ε-selection | Mathematics | Banach space | MATHEMATICS | acyclic upper semicontinuous epsilon-selection | delta-sun

Journal Article

Mathematical Notes, ISSN 0001-4346, 1/2003, Volume 73, Issue 1, pp. 142 - 147

Journal Article

Mathematical Notes, ISSN 0001-4346, 1/2002, Volume 71, Issue 1, pp. 236 - 244

In this paper, it is shown that there are no uniformly continuous multiplicative $$\varepsilon $$ -selections from $$C[0;1]$$ on the set of generalized...

Mathematics, general | Mathematics | Banach space | generalized rational approximation | uniformly continuous $$\varepsilon $$ -selection | Lipschitzian selection | Uniformly continuous ε-selection | Generalized rational approximation | MATHEMATICS | uniformly continuous epsilon-selection

Mathematics, general | Mathematics | Banach space | generalized rational approximation | uniformly continuous $$\varepsilon $$ -selection | Lipschitzian selection | Uniformly continuous ε-selection | Generalized rational approximation | MATHEMATICS | uniformly continuous epsilon-selection

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 1/1992, Volume 114, Issue 1, pp. 287 - 293

Some complete and some partial characterizations of continua are obtained in terms of the existence of an ε-selection on one or another of their hyperspaces...

Hyperspace | Dendrites | Continuous functions | Retract | A-triodic | Hereditarily unicoherent | Selection(ε–selection) | ANR | Indecomposable continuum | Contractible (crANR) | Peano continuum | Arc-like | Dendroid | Dendrite | DENDRITE, DENDROID | MATHEMATICS, APPLIED | RETRACT | INDECOMPOSABLE CONTINUUM | PEANO CONTINUUM | HEREDITARILY UNICOHERENT | ARC-LIKE | MATHEMATICS | SELECTION (EPSILON-SELECTION) | HYPERSPACE | A-TRIODIC | CONTRACTILE (CRANR)

Hyperspace | Dendrites | Continuous functions | Retract | A-triodic | Hereditarily unicoherent | Selection(ε–selection) | ANR | Indecomposable continuum | Contractible (crANR) | Peano continuum | Arc-like | Dendroid | Dendrite | DENDRITE, DENDROID | MATHEMATICS, APPLIED | RETRACT | INDECOMPOSABLE CONTINUUM | PEANO CONTINUUM | HEREDITARILY UNICOHERENT | ARC-LIKE | MATHEMATICS | SELECTION (EPSILON-SELECTION) | HYPERSPACE | A-TRIODIC | CONTRACTILE (CRANR)

Journal Article

1997, LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS, Volume 452, 14

Let M be a Hausdorff compact topological space, let C(M) be the Banach space of the continuous on M functions Supplied with the supremum norm and let V subset...

Haar condition | worst case approximation | set-valued functions | Chebyshev approximation | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | continuous epsilon-selection

Haar condition | worst case approximation | set-valued functions | Chebyshev approximation | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | continuous epsilon-selection

Book Chapter

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