**Mamoru Nunokawa 1, Janusz Sokół <sup>2</sup> and Nak Eun Cho 3,\***


Received: 11 October 2018; Accepted: 16 November 2018; Published: 19 November 2018

**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

**MSC:** 30C45; 30C80
