On a Closely Related Class Involving Spirallike Functions with Respect to a Boundary Point

• Published in: Mediterranean journal of mathematics 2020-06, Vol.17 (3), Article 92
• Main Author: Sivasubramanian, S.
• Format: Article
• Language: English
• Subjects: Analytic functions; Domains; Mathematics; Mathematics and Statistics
• ISSN: 1660-5446; 1660-5454
• DOI: 10.1007/s00009-020-01529-z

In 1981, Robertson [ 16 ] pointed out that although the class of starlike functions with respect to order α ( 0 ≤ α < 1 ) has been explored extensively by many authors over a long period of time, not much seems to be known about the class of analytic functions G ( z ) that map the open unit disc Δ onto a domain D that are starlike with respect to a boundary point. This breakthrough concept was introduced by him. Following this work, there are interesting articles (not more than two dozen in almost 4 decades) that have appeared as shown in the literature. However, an extensive exploration is yet to be done on this concept. In this present investigation, a new class of functions based on the concept of spirallike domains with respect to a boundary point introduced by Aharanov et al. [ 2 ] is considered. Further, a systematic investigation of the class under consideration is being done in this article. The author sincerely expects that this article might fetch a direction to consider other related classes in this concept in the foreseeable future.