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.

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. ...

Let A(ω) be the class of analytic functions of the form: f(z) = (z − ω) + ∞ ∑ k=2 ak(z − ω) defined on the open unit disk U = {z : |z| < 1} normalized with f(ω) = 0, f ′(ω)−1 = 0 and ω is an arbitrary fixed point in U. In this paper, we define a subclass of ω − α − uniform starlike and convex functions by using a more generalized form of Ruschewey derivative operator. Several properties such as...