In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

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, ...

n=2 anz n which are analytic in the open unit disk U := {z ∈ C : |z| < 1}. By S and C we denote the subclasses of functions in A which are univalent and convex in U, respectively. Let P be the well-known Carathéodory class of normalized functions with positive real part in U and let P(λ), 0 ≤ λ < 1 be the subclass of P consisting of functions with real part greater than λ. The Hadamard product ...

It is well known [28] that a number of important classes of univalent functions (e.g. convex, starlike) are related through their derivatives by functions with positive real part. These functions play an important part in problem from signal theory, in moment problems and in constructing quadrature formulas, see Ronning [97] and the references cited therein for some recent applications. In this...

The purpose of the present paper is to study a new subclass of harmonic univalent functions associated with fractional calculus operator. We obtain coefficient conditions, distortion bounds and extreme points for this class and discuss a class preserving integral operator. We also show that the class studied in this paper is closed under convolution and convex combination. The results obtained ...

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...

We give a control-theoretic proof of Pommerenke's result on the parametric representation of normalized univalent functions in the unit disk as solutions of the Loewner diierential equation. The method consists in combining a classical result on nite-dimensional control-linear systems with Montel's theorem on normal families. x1 Introduction We rst recall some important subsets of the vector sp...

Let $\Omega$ be a subdomain of $\mathbb{C}$ and let $\mu$ positive Borel measure on $\Omega$. In this paper, we study the asymptotic behavior eigenvalues compact Toeplitz operators $T\_\mu$ acting Bergman spaces $(\lambda n(T\mu))$ decreasing sequence $T\_\mu$, $\rho$ an increasing function such that $\rho (n)/n^A$ is for some $A>0$. We give explicit necessary sufficient geometric condition in ...