Starlike and convexity properties for pvalent solutions of the Shah differential equation 

Author 
m.m.sheremeta@gmail.com, yurkotrukhan@gmail.com
Ivan Franko National University of Lviv, Lviv, Ukraine

Abstract 
The starlikeness and the convexity in the unit disc
and the growth of an entire function
$f(z)=z^p+\sum\nolimits_{n=p+1}^{\infty}f_n z^n$, $p\in{\Bbb N}$,
satisfying the differential equation
$z^2 w''+(\beta_0z^2+\beta_1z)w'+(\gamma_0 z^2+\gamma_1 z+\gamma_2) w=0$
($\beta_0,\,\beta_1,\,\gamma_0,\,\gamma_1,\,\gamma_2$ are complex parameters) are studied.

Keywords 
starlikeness; convexity; entire function; differential equation

DOI 
doi:10.15330/ms.48.1.1423

Reference 
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transl.: AMS: Translations of Mathematical monograph, 26 (1969), 676p.
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Pages 
1423

Volume 
48

Issue 
1

Year 
2017

Journal 
Matematychni Studii

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