arXiv subjects
Publications and source records attributed to Ikkei Hotta.
In this paper we confirm that several crucial theorems due to Pommerenke and Becker for the theory of Loewner chains work well without normalization on the complex-valued first coefficient. As applications of those considerations, some new univalent and quasiconformal extension criteria are given in the last section.
This article contains several results for λ-Robertson functions, i.e., analytic functions $f$ defined on the unit disk $D$ satisfying $f(0) = f'(0)-1=0$ and $Re e^{-iλ} {1+zf"(z)/f'(z)} > 0$ in $D$, where $λε(-π/2,π/2)$. We will discuss about conditions for boundedness and quasiconformal extension of Robertson functions. In the last section we provide another proof of univalence for Robertson functions by using the theory of Löwner chains.
In this note we investigate the inclusion relationship between the class of strongly starlike functions of order alpha and type beta and the class of strongly convex functions of order alpha and type beta which are subclass of normalized analytic functions defined on the unit disk. Some applications of our main result are also presented which contains various classical results for the typical subclasses of starlike and convex functions.
Ruscheweyh extended the work of Becker and Ahlfors on sufficient conditions for a normalized analytic function on the unit disk to be univalent there. In this paper we refine the result to a quasiconformal extension criterion with the help of Becker's method. As an application, a positive answer is given to an open problem proposed by Ruscheweyh.