New subclasses of Ozaka's convex functions

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Sciences, Urmia University, P. O. Box 165, Urmia, Iran

Abstract

Let SL(\uplambda) and CVL(\uplambda) be the classes of functions
f, analytic in the unit disc \Updelta={z:|z|<1}, with the
normalization f(0)=f(0)1=0, which satisfies the conditions
zf(z)f(z)(1+z)\uplambdaand(1+zf(z)f(z))(1+z)\uplambda(0<\uplambda1),
where is the subordination relation, respectively. The classes
SL(\uplambda) and CVL(\uplambda) are subfamilies of the known classes of strongly starlike and convex functions of order \uplambda. We consider  the relations between SL(\uplambda), CVL(\uplambda) and other classes geometrically defined. Also, we obtain the sharp radius of convexity for functions belonging to SL(\uplambda) class. Furthermore,  the norm of pre-Schwarzian derivatives  and univalency of functions f which satisfy the condition
{1+zf(z)f(z)}<1+\uplambda2\mypz\Updelta,
are considered.

Keywords

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Volume 14, Issue 3
March 2023
Pages 189-199
  • Receive Date: 18 July 2022
  • Revise Date: 30 May 2022
  • Accept Date: 12 October 2022