The titled Carathodory class and its applications

Abstract

This survey mainly deals with the tilted Carath{é}odory class by angle $\lambda$ (denoted by ${\mathcal{P}}_{\lambda }$) an element of which maps the unit disc into the tilted right half-plane $\{w:\Re e^{i\lambda }w>0\}$. Firstly we will characterize ${\mathcal{P}}_{\lambda }$ from different aspects. In section 3, various estimates of functionals over ${\mathcal{P}}_{\lambda }$ are deduced from the known corresponding estimates of ${\mathcal{P}}_0$ or elementary functional analysis. Finally some subsets of analytic functions related to ${\mathcal{P}}_{\lambda }$ including close-to-convex functions with argument $\lambda$, $\lambda$-spirallike functions, $\lambda$-Robertson functions and analytic functions whose derivative is in ${\mathcal{P}}_{\lambda }$ are also considered as applications

17 pages

References in corpus (2)

• Subordination Problems of Robertson functions
• Boundedness, univalence and quasiconformal extension of Robertson functions

Cited by in corpus (2)

• Subordination Problems of Robertson functions
• Boundedness, univalence and quasiconformal extension of Robertson functions