On entire solutions of a differential equation |
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| Author |
Institute of Applied Problems of Mechanics and Mathematics, 3b Naukova str., Lviv, Ukraine
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| Abstract |
We study conditions on constant coefficients of the differential equation $$ z^2 w''+(b_0 z^2+b_1 z) w'+(g_0 z^2+g_1 z+g_2)w=0, $$ under which an entire solution $f$ of this equation and all its derivatives $f', f'',\dots$ are close-to-convex in the unit disk.
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| Keywords |
differential equations with constant coefficients, entire solutions, close-to-convex functions, unit disk, geometric function theory, derivatives of entire functions, analytic function properties
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| DOI |
doi:10.30970/ms.14.1.54-58
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Reference |
1. Shah S. M. Univalence of a function $f$ and its successive derivatives when $f$ satisfies a differential equation, II, J. Math. anal. and appl. 142 (1989), 422--430.
2. Шеремета З. М., О свойствах целых решений одного дифференциального уравнения, Дифф. урав. 36 (2000), № 6, 921–929. 3. Goodman A. W. Univalent function, Vol. II, Mariner Publishing Co., 1983, 158 pp. |
| Pages |
54-58
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| Volume |
14
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| Issue |
1
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| Year |
2000
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| Journal |
Matematychni Studii
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