The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

The Fekete-Szegö Problem for p-Valently Janowski Starlike and Convex Functions

For p-valently Janowski starlike and convex functions defined by applying subordination for the generalized Janowski function, the sharp upper bounds of a functional |a p2 − μa 2 p1 | related to the Fekete-Szegö problem are given.

Parabolic starlike mappings of the unit ball $B^n$

Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$  where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...

Relations between the Generalized Bessel Functions and the Janowski Class

We are interested in finding the sufficient conditions on A , B , λ , b and c which ensure that the generalized Bessel functions uλ := uλ ,b,c satisfies the subordination uλ (z) ≺ (1+Az)/(1+Bz) . Also, conditions for which uλ (z) to be Janowski convex, and zuλ (z) to be Janowski starlike in the unit disk D = {z ∈ C : |z| < 1} are obtained. Mathematics subject classification (2010): 34B30, 33C10...

Harmonic Mappings Related to Starlike Function of Complex Order Α

Let SH be the class of harmonic mappings defined by SH = { f = h(z) + g(z) | h(z) = z + ∞ ∑ n=2 anz , g(z) = ∞ ∑

On Janowski Starlike Functions