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

Abstract

In 1981, Robertson [16] pointed out that although the class of starlike functions with respect to order $\alpha ( 0 \le \alpha <1)$ 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 $\Delta$ onto a domain ${\mathcal {D}}$ 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.