On a Length Problem for Univalent Functions

Mamoru Nunokawa, Janusz Sokół and Nak Eun Cho
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Mamoru Nunokawa: Department of Mathematics, Gunma University, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, Japan
Janusz Sokół: Faculty of Mathematics and Natural Sciences, University of Rzeszów, 1 Prof. St. Pigoń Street, 35-310 Rzeszów, Poland
Nak Eun Cho: Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Pusan 608-737, Korea

Mathematics, 2018, vol. 6, issue 11, 1-8

Abstract: 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: analytic functions; starlike functions; univalent functions; length problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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