Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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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)
  • Received : 2013.10.25
  • Accepted : 2014.04.11
  • Published : 2015.06.23
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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.

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