We find the radius of starlikeness order $\alpha$, $0\leq \alpha<1$, normalized analytic functions $f$ on unit disk satisfying either $Re(f(z)/g(z))>0$ or $\left|(f(z)/g(z))-1\right|<1$ for some close-to-star function $g$ with $Re(g(z)/(z+z^2/2))>0$ as well class $Re(f(z)/(z+z^2/2))>0$. Several other radii such univalence and parabolic are shown to be same app...

Let A consists of analytic functions f :

The asymptotic behaviour, with respect to the large order, of radii starlikeness two types normalised Bessel functions is considered. We derive complete expansions for and provide recurrence relations coefficients these expansions. proofs rely on notion Rayleigh sums inversion. techniques employed in paper could be useful treat similar problems where inversion involved.

This paper aims to provide sufficient conditions for starlikeness and convexity of Hadamard product (convolution) certain multivalent analytic functions with positive real parts. Moreover, the a integral operator other convolution results are also considered.

Copyright q 2010 Gejun Bao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We determine the condition on α, μ, β, and λ for which | 1−α z/f z μ α zf ′ z /f z z/f z − 1| < λ implies f z ∈ S∗ β , where S∗ β is the class of st...

In this paper, we derive conditions on the parameters a, b, c so that the function zF (a, b; c; z) is starlike in D, where F (a, b; c; z) denotes the classical hypergeometric function. We give some consequences of our results including some mapping properties of convolution operator.