In this paper, we introduce two subclasses Ωp(α) and Λ ∗ p(α) of meromorphic pvalent functions in the punctured diskD = {z : 0 < |z| < 1}. Coefficient inequalities, distortion theorems, the radii of starlikeness and convexity, closure theorems and Hadamard product ( or convolution) of functions belonging to these classes are obtained.

We consider strongly starlikeness of order α of functions f(z)= z+an+1zn+1 +··· which are analytic in the unit disc and satisfy the condition of the form ∣∣∣∣f ′(z) ( z f(z) )1+μ −1 ∣∣∣∣< λ, 0< μ < 1, 0< λ< 1.

The Wright’s generalized hypergeometric function is used here to introduce a new class of p-valent functions WT p(λ, α, β) defined in the open unit disc and investigate its various characteristics. Further we obtain distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity of functions belonging to the class WT p(λ, α, β).

Let h be a nonvanishing analytic function in the open unit disc with id="M2"> 0 = 1 . Consider class consisting of normalized functions id="M3"> f whose ratios id="M4"> z / g , id="M5"> <mi...

In this paper, we first modify one of the most famous theorems on principle differential subordination to hold true for normalized analytic functions with a fixed initial Taylor-Maclaurin coefficient. By using modified form, generalize and improve several results, which appeared recently in literature geometric function theory complex analysis. We also prove some simple conditions starlikeness,...

We determine the sufficient conditions for function f(z) = z + a2z2 ... to be starlike of order 1/2, which shows also starlikeness f.

Let A,B,D,E ∈ [−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0) = 1. Conditions on A, B, D, and E are determined so that 1 + βzp′(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the expressions 1 + β(zp′(z)/p(z)) and 1 + β(zp′(z)/p2(z)). These results are then applied to obtain s...

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| &lt; 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...