In this paper, we introduce a new class of analytic functions defined by a new convolution operator La (α, β). The new class of analytic functions Σ a,t α,β (ρ; h) in U ∗ = {z : 0 < |z| < 1} is defined by means of a hypergeometric function with an integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. The authors also introduces and investigates variou...

‎In this paper,  the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.

The pre-Schwarzianand Schwarzian derivatives of analytic functions f are defined in U, where U is the open unit disk. pre-Schwarzian as well popular tools for studying geometric properties mappings. These can also be used to obtain either necessary or sufficient conditions univalence a function f. Because computational difficulty, norm has received more attention than norm. It applications theo...

In this paper we consider two functionals of the Fekete–Szegö type: Φ f (μ)=a 2 a 4 -μa 3 and Θ for analytic functions f(z)=z+a z +a +..., z∈Δ, (Δ={z∈ℂ:|z|<1}) real numbers μ. For which is univalent convex in direction imaginary axis, find sharp bounds (μ) (μ). It possible to transfer results onto class

Let A denote the class of analytic functions f z defined in the unit disc E {z : |z| < 1} and satisfying the conditions f 0 0, f ′ 0 1. Let S denote the subclass of A consisting of univalent functions in E, and let S∗ and C be the subclasses of Swhich contains, respectively, star-like and convex in Bazilevič 1 introduced the class B α, β, h, g as follows. Let f ∈ A. Then, f ∈ B α, β, h, g , α, ...

then we say that p is the Catathéodory function. LetA denote the class of all functions f analytic in the open unit disk U {z : |z| < 1} with the usual normalization f 0 f ′ 0 − 1 0. If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f z ≺ g z , if g is univalent, f 0 g 0 and f U ⊂ g U . For 0 < α ≤ 1, let STC α and STS α denote the classes of functions f ∈ A whic...

in this paper we introduce and investigate a certain subclass of univalentfunctions which are analytic in the unit disk u.such results as coecientinequalities. the results presented here would provide extensions of those givenin earlier works.