THE TILTED CARATHÉODORY CLASS AND ITS APPLICATIONS

Title & Authors
THE TILTED CARATHÉODORY CLASS AND ITS APPLICATIONS
Wang, Li-Mei;

Abstract
This paper mainly deals with the tilted Carath$\small{\acute{e}}$odory class by angle $\small{{\lambda}}$ $\small{{\in}}$ ($\small{-{\pi}/2}$, $\small{{\pi}/2}$), denoted by $\small{P{\lambda}}$) an element of which maps the unit disc into the tilted right half-plane {<$\small{{\omega}}$ : Re $\small{e^{i{\lambda}}{\omega}}$ > 0}. Firstly we will characterize $\small{P{\lambda}}$ from different aspects, for example by subordination and convolution. Then various estimates of functionals over $\small{P{\lambda}}$ are deduced by considering these over the extreme points of $\small{P{\lambda}}$ or the knowledge of functional analysis. Finally some subsets of analytic functions related to $\small{P{\lambda}}$ including close-to-convex functions with argument $\small{{\lambda}}$, $\small{{\lambda}}$-spirallike functions and analytic functions whose derivative is in $\small{P{\lambda}}$ are also considered as applications.
Keywords
the tilted Carath$\small{\acute{e}}$odory class;$\small{{\lambda}}$-spirallike functions;close-to-convex functions with argument $\small{{\lambda}}$;convolution;subordination;
Language
English
Cited by
1.
Subordination Problems of Robertson Functions,;

Kyungpook mathematical journal, 2011. vol.51. 4, pp.411-417
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