Domains in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>with conically accessible boundary

Liczberski, Piotr; Starkov, Victor V.

doi:10.1016/j.jmaa.2013.06.029

Cited by 9 publications

(22 citation statements)

References 10 publications

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“…Note that by Theorem 2 the set D under the given conditions is a γ-accessible domain, where γ = min{α, β}. It follows that D is starlike domain (see [4]). Suppose that D is not an (α, β)-accessible domain.…”

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confidence: 93%

“…In [1,2,3] (α, β)-accessible domains were studied as a generalization of α-accessible domains (see [4]). In [2], it was shown that the domain D is (α, β)-accessible with respect to 0 if and only if, for each point p ∈ ∂D, the unbounded cone…”

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confidence: 99%

“…If in the Definition 1 α = β, then we obtain the definition of α-accessible domain with respect to 0 (see [4]). …”

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confidence: 99%

“…An (α, β)-accessible domain is γ-accessible (γ = min{α, β}), and starlike with respect to 0, as a consequence (see [4]). In the case α = β = 0 the class of (0, 0)-accessible domains coincides with the class of starlike with respect to 0 domains (see [5]).…”

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confidence: 99%

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Necessary and Sufficient Condiyions of (Α, Β)–accessibility of Domain in Nonsmooth Case

Amozova¹

2015

Issues of Analysis

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Abstract. In [1], [2] (α, β)-accessible domains in C were defined and investigated, and the criterion of (α, β)-accessibility in a smooth case was obtained. (α, β)-accessible domains are starlike, γ-accessible (γ = min{α; β}), and satisfy the so-called "cone condition" (i. e. the domains are conically accessible from the interior), which is important for applications, such as the theory of integral representations of functions, imbedding theorems, the questions of the boundary behavior of functions, the solvability of Dirichlet problem. In this paper the author obtains the necessary and some sufficient conditions of (α, β)-accessibility of domain in nonsmooth case.

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confidence: 93%

mentioning

confidence: 99%

“…If in the Definition 1 α = β, then we obtain the definition of α-accessible domain with respect to 0 (see [4]). …”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Necessary and Sufficient Condiyions of (Α, Β)–accessibility of Domain in Nonsmooth Case

Amozova¹

2015

Issues of Analysis

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“…Introduction. In [6] (see also [7]) α-accessible domain, α ∈ [0, 1), were introduced and studied. A domain Ω ⊂ R n , 0 ∈ Ω, is called α-accessible, if for every point p ∈ ∂Ω there exists a number r = r(p) > 0 such that the cone…”

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confidence: 99%

Plane Domains With Special Cone Condition

Anikiev¹

2014

Issues of Analysis

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Abstract. The paper considers the domains with cone condition in C. We say that domain G satisfies the (weak) cone con- [4]). In the paper of P. Liczberski and V. V. Starkov, α-accessible domains were considered, α ∈ [0, 1), -the domains, accessible at every boundary point by the cone with symmetry axis on {pt : t > 1}. Unlike the paper of P. Liczberski and V. V. Starkov, here we consider domains, accessible outside by the cone, which symmetry axis inclined on fixed angle ϕ to the {pt : t > 1}, 0 < ∥ϕ∥ < < π/2. In this paper we give criteria for this class of domains when the boundaries of domains are smooth, and also give a sufficient condition when boundary is arbitrary. This article is the full variant of [5], published without proofs.

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On the Fekete and Szegö Inequality for a Subclass of Strongly Starlike Mappings of Order $${\varvec{\alpha }}$$ α

Luo

2017

Results Math

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Domains inRnwith conically accessible boundary

Cited by 9 publications

References 10 publications

Necessary and Sufficient Condiyions of (Α, Β)–accessibility of Domain in Nonsmooth Case

Necessary and Sufficient Condiyions of (Α, Β)–accessibility of Domain in Nonsmooth Case

Plane Domains With Special Cone Condition

On the Fekete and Szegö Inequality for a Subclass of Strongly Starlike Mappings of Order $${\varvec{\alpha }}$$ α

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