A parabolic starlike function f of order ρ in the unit disk is characterized by the fact that the quantity z f ′(z)/ f (z) lies in a given parabolic region in the right half-plane. Denote the class of such functions by PS∗(ρ). This class is contained in the larger class of starlike functions of order ρ. Subordination results for PS∗(ρ) are established, which yield sharp growth, covering, and di...

Let D := {z ? C : |z| < 1} be the open unit disk, and h 1 two analytic functions in D. Suppose that f = + ?g is a harmonic mapping with usual normalization h(0) 0 g(0) h'(0) 1. In this paper, we consider mappings by restricting its part to family of convex one direction and, particular, starlike. Some sharp optimal estimates for coefficient bounds, growth, covering area bounds are investigat...

The aim of present investigation is to study a new class analytic function related with the Sokol-Nunokawa class. We derived relationships this strongly starlike functions and obtained many interesting results.

and Applied Analysis 3 Theorem 1.3 see 12 . Let c2k c2k 1 μ k/k!, μ ∈ 0, 1 . For any positive integer n and 0 < θ < π , then i ∑n k 0 ck cos kθ > 0 if and only if 0 < μ ≤ μ0, ii ∑2n 1 k 1 ck sin kθ > 0 if and only if 0 < μ ≤ μ0, iii ∑2n k 1 ck sin kθ > 0 if 0 < μ ≤ 1/2. Here μ0 0.691556 · · · is the unique root in 0, 1 of ∫3π/2 0 cos t t1−μ dt 0. 1.6 2. Main Results For our purpose, it will be ...