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http://dx.doi.org/10.5666/KMJ.2015.55.2.395

Radii of Starlikeness and Convexity for Analytic Functions with Fixed Second Coefficient Satisfying Certain Coefficient Inequalities  

MENDIRATTA, RAJNI (Department of Mathematics, University of Delhi)
NAGPAL, SUMIT (Department of Mathematics, University of Delhi)
RAVICHANDRAN, V. (Department of Mathematics, University of Delhi)
Publication Information
Kyungpook Mathematical Journal / v.55, no.2, 2015 , pp. 395-410 More about this Journal
Abstract
For functions $f(z)=z+a_2z^2+a_3z^3+{\cdots}$ with ${\mid}a_2{\mid}=2b$, $b{\geq}0$, sharp radii of starlikeness of order ${\alpha}(0{\leq}{\alpha}<1)$, convexity of order ${\alpha}(0{\leq}{\alpha}<1)$, parabolic starlikeness and uniform convexity are derived when ${\mid}a_n{\mid}{\leq}M/n^2$ or ${\mid}a_n{\mid}{\leq}Mn^2$ (M>0). Radii constants in other instances are also obtained.
Keywords
starlike functions; convex functions; uniformly convex functions; parabolic starlike functions; radius problems; fied second coefficient;
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