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

• Journal title : Kyungpook mathematical journal
• Volume 55, Issue 2,  2015, pp.395-410
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2015.55.2.395
Title & Authors
Radii of Starlikeness and Convexity for Analytic Functions with Fixed Second Coefficient Satisfying Certain Coefficient Inequalities
MENDIRATTA, RAJNI; NAGPAL, SUMIT; RAVICHANDRAN, V.;

Abstract
For functions $\small{f(z)=z+a_2z^2+a_3z^3+{\cdots}}$ with $\small{{\mid}a_2{\mid}=2b}$, $\small{b{\geq}0}$, sharp radii of starlikeness of order $\small{{\alpha}(0{\leq}{\alpha}}$<$\small{1)}$, convexity of order $\small{{\alpha}(0{\leq}{\alpha}}$<$\small{1)}$, parabolic starlikeness and uniform convexity are derived when $\small{{\mid}a_n{\mid}{\leq}M/n^2}$ or $\small{{\mid}a_n{\mid}{\leq}Mn^2}$ (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;
Language
English
Cited by
1.
Radius Problems for Ratios of Janowski Starlike Functions with Their Derivatives, Bulletin of the Malaysian Mathematical Sciences Society, 2016
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