Mathematics (Nov 2018)

On a Length Problem for Univalent Functions

  • Mamoru Nunokawa,
  • Janusz Sokół,
  • Nak Eun Cho

DOI
https://doi.org/10.3390/math6110266
Journal volume & issue
Vol. 6, no. 11
p. 266

Abstract

Read online

Let g be an analytic function with the normalization in the open unit disk. Let L ( r ) be the length of g ( { z : | z | = r } ) . In this paper we present a correspondence between g and L ( r ) for the case when g is not necessary univalent. Furthermore, some other results related to the length of analytic functions are also discussed.

Keywords