On a class of starlike functions related to a shell‐like curve connected with Fibonacci numbers

In this paper we investigate an interesting subclass $\mathcal{SL}$ of analytic univalent functions in the open unit disc on the complex plane. This class was introduced by Sokól [J. Sokól, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis 175 (1999) 111–116]. The class $\mathcal{SL}$ is strongly related to the class $\mathcal{KSL}$ considered earlier by the authors of the present work in their paper [J. Dziok, R. K. Raina, J. Sokól, Certain results for a class of convex functions related to shell‐like curve connected with Fibonacci Numbers, Comput. Math. Appl. 61 (2011) 2606–2613]. Apart from furnishing some genuine remarks, we present certain new results for the class $\mathcal{SL}$ of functions, and also mention some relevant cases for this function class.