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 ...

Let f(z) = z + ∑(n=2)(∞) (a)n(z) (n) be analytic in the unit disk with the second coefficient a2 satisfying |a2| = 2b, 0 ≤ b ≤ 1. Sharp radius of Janowski starlikeness is obtained for functions f whose nth coefficient satisfies |a(n)| ≤ cn + d (c, d ≥ 0) or |a(n)| ≤ c/n  (c > 0 and n ≥ 3). Other radius constants are also obtained for these functions, and connections with earlier results are made.

We investigate the new class H b (α, β) of analytic functions with Koebe type. The subordination, superordination, best dominant result for that class was obtain. And by making use of Jack's Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class H b (α, β) of n-fold symmetric analytic functions of Koebe type. Relevant...