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FEKETE-SZEGÖ PROBLEM FOR SUBCLASSES OF STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC POINTS

  • Shanmugam, T.N. (Department of Mathematics, College of Engineering, Anna University) ;
  • Ramachandram, C. (Department of Mathematics, College of Engineering, Anna University) ;
  • Ravichandran, V. (School of Mathematical Sciences, Universiti Sains Malaysia)
  • Published : 2006.08.01

Abstract

In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.

Keywords

analytic functions;starlike functions;convex functions;subordination;coefficient problem;$Fekete-Szeg\"{o}$ inequality

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