For a natural number $n\geq 2$, the function $\phi_{n\mathcal{L}}(z)=1+nz/(n+1)+z^n/(n+1)$ maps open unit disk onto domain bounded by an epicycloid with $(n-1)$ cusps. A class of starlike functions associated $\phi_{n\mathcal{L}}$ is defined in and its sharp bounds on initial coefficients, various inclusion relations radii problems related to other subclasses are investigated. As application, c...

By using the method of differential subordinations, we derive some sufficient conditions for strongly starlike functions associated with a linear operator. All these results presented here are sharp.

In this paper we introduce a class of strongly starlike functions of order α and type β with respect to symmetric points and investigate the neighborhoods and coefficients bounds of such functions.

We introduce universally convex, starlike and prestarlike functions in the slit domain C \ [1,∞), and show that there exists a very close link to completely monotone sequences and Pick functions.

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We consider meromorphic starlike univalent functions that are also bi-starlike and find Faber polynomial coefficient estimates for these types of functions. A function is said to be bi-starlike if both the function and its inverse are starlike univalent. Consider ...

In the present paper, we introduce and investigate some properties of two subclasses $ Lambda_{n}( lambda , beta ) $ and $ Lambda_{n}^{+}( lambda , beta ) $;  meromorphic and starlike  functions of order $ beta $. In particular, several inclusion relations, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes.

An interesting criterion was given by Tuneski [N. Tuneski, On the quotient of the representations of convexity and starlikeness, Math. Nachr. 248–249 (2003) 200–203] for the analytic functions to be in the class S 1⁄21þAz 1þBz and its subclasses, where 1 6 B < A 6 1. This result is an extension of an earlier result of Silverman [H. Silverman, Convex and starlike criteria, Int. Math. Math. Sci. ...