On the Properties of a New Class of α-Close-to-Convex Functions (original) (raw)

Some radius properties for a class of alpha-close-to-convex functions

AIP Conference Proceedings, 2015

We define) , (δ α K G as the class of α-close-to-convex functions satisfying () () δ α > ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ z g z f e i ' ' Re for π α ≤ , δ α > cos and () z z g − = 1 1 ' with () K z g ∈. For this class of functions, we obtain the basic properties such as representation theorem, coefficient bound and distortion theorem. We also find the rotation theorem when

Some subclasses of close-to-convex functions

Annales Polonici Mathematici

For α ∈ [0, 1] and β ∈ (−π/2, π/2) we introduce the classes C β (α) defined as follows: a function f regular in U = {z : |z| < 1} of the form f (z) = z + ∞ n=1 anz n , z ∈ U , belongs to the class C β (α) if Re{e iβ (1 − α 2 z 2)f (z)} > 0 for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in C β (α) are examined.

A New Subclass of Close-To-Convex Functions

2016

In this work, we introduce and investigate an interesting subclass Xt(γ) of analytic and close-to-convex functions in the open unit disk U. For functions belonging to the class Xt(γ), we drive several properties including coefficient estimates, distortion theorems, covering theorems and radius of convexity.

A generalized class of close –to- convex functions

1983

In this papeTl, ue intv,odLtce d, neu cLass K, of anaLyti/c ffi&lffis and note that .bhe class K of close-to-eonfiex functlons t)s contained in it. The famous Biebevbach aonjec'bure, uhich was preui.oualg knaun t;o be tz:ue fon close-to-conDeff functions, 'holfls also fot' the elass K.,. Distortion l;heoy'ems and Arclength problem are 'tru)esti,gdted, Let f (z) = z + arzz+ " be an analytic function in the unit disc E-{z: lzlcf}. The funcrion f(z) is said to be close-toconvert ln E, if there exists a function g(z), such that for zeE,

On certain properties for a subclass of close-to-convex functions

Journal of Classical Analysis, 2012

In the present paper, we introduce and investigate an interesting subclass K λ s (h) of analytic and close-to-convex functions in the open unit disk U. For functions belonging to the class K λ s (h) , we derive several properties as the convolution, the coefficient bounds, the covering theorem, the inclusion relationships as well as distortion theorem. The various results presented here would generalize many known recent results.

Extremal Properties Of Generalized Class Of Close-To-Convex Functions

2011

Let Gα ,β (γ ,δ ) denote the class of function f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) , β ∈ı and γ ∈ı (0 ≤γ <α ) where δ ≤ π and α cosδ −γ > 0 . In this paper, we determine some extremal properties including distortion theorem and argument of f ′( z ) .

On Certain Generalizations of Close-to-convex Functions

Earthline Journal of Mathematical Sciences, 2020

The aim of this article is to introduce and study certain subclasses of analytic functions and we investigate various properties of these classes such as inclusion properties and convex convolution preserving properties. Also, some related applications are discussed.

On a Subclass of Close-to-Convex Functions

Bulletin of the Iranian Mathematical Society, 2018

In this paper, we introduce a subclass of close-to-convex functions defined in the open unit disk. We obtain the inclusion relationships, coefficient estimates and Fekete-Szego inequality. The results presented here would provide extensions of those given in earlier works.

A class of strongly close-to-convex functions

Boletim da Sociedade Paranaense de Matemática

In this paper, we study a class of strongly close-to-convex functions f(z)f(z)f(z) analytic in the unit disk mathbbU\mathbb{U}mathbbU with f(0)=0,fprime(0)=1f(0)=0,f^{\prime }(0)=1f(0)=0,fprime(0)=1 satisfying for some convex function g(z)g(z)g(z) the condition that\begin{equation*}\frac{zf^{\prime }(z)}{g(z)}\prec \left( \frac{1+Az}{1+Bz}\right) ^{m}\end{equation*}%\begin{equation*}\left( -1\leq A\leq 1,-1\leq B\leq 1\ \left( A\neq B\right) ,0