[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2012.49.4.671

THE TILTED CARATHÉODORY CLASS AND ITS APPLICATIONS

Wang, Li-Mei (Division of Mathematics Graduate School of Information Sciences Tohoku University)

Publication Information

Journal of the Korean Mathematical Society / v.49, no.4, 2012 , pp. 671-686 More about this Journal

Abstract

This paper mainly deals with the tilted Carath $\acute{e}$ odory class by angle ${\lambda}$ ${\in}$ ( $-{\pi}/2$ , ${\pi}/2$ ), denoted by $P{\lambda}$ ) an element of which maps the unit disc into the tilted right half-plane {< ${\omega}$ : Re $e^{i{\lambda}}{\omega}$ > 0}. Firstly we will characterize $P{\lambda}$ from different aspects, for example by subordination and convolution. Then various estimates of functionals over $P{\lambda}$ are deduced by considering these over the extreme points of $P{\lambda}$ or the knowledge of functional analysis. Finally some subsets of analytic functions related to $P{\lambda}$ including close-to-convex functions with argument ${\lambda}$ , ${\lambda}$ -spirallike functions and analytic functions whose derivative is in $P{\lambda}$ are also considered as applications.

Keywords

the tilted Carath $\acute{e}$ odory class; ${\lambda}$ -spirallike functions; close-to-convex functions with argument ${\lambda}$ ; convolution; subordination;

Citations & Related Records

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