Geodesic
About planar $(\alpha,\beta)$--accessible domains
Problemy analiza, Tome 3 (2014) no. 2, pp. 3-15

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The article is devoted to the class $A^{\alpha,\beta}_{\rho}$ of all $(\alpha,\beta)$–accessible with respect to the origin domains $D,$ $\alpha,\beta\in[0,1),$ possessing the property\thinspace $\rho=\min\limits_{p\in\partial D}|p|,$\thinspace where\thinspace $\rho\thinspace\in \thinspace(0,+\infty)$ is a fixed number. We find the maximal set of points $a$ such that all domains $D\in A^{\alpha,\beta}_{\rho}$ are $(\gamma,\delta)$–accessible with respect to $a,$ $\gamma\in[0;\alpha],$ $\delta\in[0;\beta]$. This set is proved to be the closed disc of center $0$ and radius $\rho\sin\displaystyle\frac{\varphi\pi}{2},$ where $\varphi=\min\left\{\alpha-\gamma,\beta-\delta\right\}$.
Keywords: cone condition.
Mots-clés : $\alpha$–accessible domain, $(\alpha,\beta)$–accessible domain 
@article{PA_2014_3_2_a0,
     author = {K. F. Amozova and E. G. Ganenkova},
     title = {About planar $(\alpha,\beta)$--accessible domains},
     journal = {Problemy analiza},
     pages = {3--15},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2014_3_2_a0/}
}
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K. F. Amozova; E. G. Ganenkova. About planar $(\alpha,\beta)$--accessible domains. Problemy analiza, Tome 3 (2014) no. 2, pp. 3-15. http://geodesic.mathdoc.fr/item/PA_2014_3_2_a0/