This paper deals with p-valent strongly starlikeness of the class SP (α,A,B) satisfying the subordination e zf ′(z) f(z) ≺ cos z 1 +Az 1 +Bz + i sin α, f ∈ A, z ∈ ∆, 0 ≤ α < 1, −1 ≤ B < A ≤ 1. We are concerned with computing the radius results for the above mentioned class and the results that we obtained are generalizations of earlier results obtained previously by different authors. MSC: 30C4...

Let the functions q1 be analytic and let q2 be analytic univalent in the unit disk. Using the methods of differential subordination and superordination, sufficient conditions involving the Schwarzian derivative of a normalized analytic function f are obtained so that either q1 z ≺ zf ′ z /f z ≺ q2 z or q1 z ≺ 1 zf ′′ z /f ′ z ≺ q2 z . As applications, sufficient conditions are determined relati...

Let for fixed n ∈ N, Σn denotes the class of function of the following form f(z) = 1 z + ∞ ∑ k=n akz , which are analytic in the punctured open unit disk ∆∗ = {z ∈ C : 0 < |z| < 1}. In the present paper we defined and studied an operator in F (z) = [ c+ 1− μ zc+1 ∫ z 0 ( f(t) t )μ tdt ] 1 μ , for f ∈ Σn and c+ 1− μ > 0.

In this paper, we mainly study the order of q-starlikeness well-known basic hypergeometric function. addition, discuss Bieberbach-type problem and second Hankel determinant for a generalized class starlike functions.