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

MENDIRATTA, RAJNI;NAGPAL, SUMIT;RAVICHANDRAN, V.

  • Received : 2013.10.25
  • Accepted : 2014.04.11
  • Published : 2015.06.23

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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Cited by

  1. Radius Problems for Ratios of Janowski Starlike Functions with Their Derivatives vol.40, pp.2, 2017, https://doi.org/10.1007/s40840-016-0363-x

Acknowledgement

Supported by : University of Delhi