UNIVALENCE CONDITIONS FOR A NEW INTEGRAL OPERATOR

2015 ◽  
Vol 1 (2) ◽  
pp. 35-37
Author(s):  
Sh. Najafzadeh ◽  
A. Ebadian ◽  
H. Rahmatan
Keyword(s):  
Integral Operator ◽  
Univalent Functions ◽  
Norm Estimates ◽  
Schwarzian Derivatives ◽  
Convex Univalent Functions

In the present paper, we will obtain norm estimates of the pre-Schwarzian derivatives for $F_{\lambda,\mu}(z)$, such that \[ F_{\lambda,\mu}(z) = \int_0^z \prod_{i=1}^{n} (f'_i(t))^{\lambda_i}\left( \frac{f_i(t)}{t} \right)^{\mu_i}dt \quad (z\in D),\] where $\lambda_i,\mu_i\in \mathbb{R}$, $\lambda_i=(\lambda_1,\lambda_2,\ldots,\lambda_n$, $\mu_i=(\mu_1,\mu_2,\ldots,\mu_n$ and $f_i$ belongs to the class of convex univalent functions $\mathcal{C}\subset \mathcal{S}$.

Applications of differential subordinations for norm estimates of an integral operator

2017 ◽  
Vol 148 (2) ◽  
pp. 281-291 ◽  
Author(s):  
Jacek Dziok ◽  
Ravinder Krishna Raina ◽  
Janusz Sokół
Keyword(s):  
Integral Operator ◽  
Univalent Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Univalent Functions ◽  
Norm Estimates ◽  
Convolution Structure ◽  
Image Position ◽  
Convex Univalent Functions ◽  
Differential Subordinations

By considering the norm of a locally univalent function given bywe obtain such norm estimates for an operator of functions involving a convolution structure of convex univalent functions with a subclass of convex functions (defined by subordination). We also obtain some inequalities concerning this norm for functions under a certain fractional integral operator. Some implications of our results are briefly pointed out in the concluding section.

scholarly journals On an integral operator for convex univalent functions

1986 ◽  
Vol 34 (2) ◽  
pp. 211-218
Author(s):  
Vinod Kumar ◽  
S. L. Shukla
Keyword(s):  
Integral Operator ◽  
Real Number ◽  
Complex Number ◽  
Univalent Functions ◽  
Corrected Version ◽  
Convex Univalent Functions ◽  
Class Of Functions

Let K (m,M) denote the class of functions regular and satisfying |1 + zf″(z)/f′(z)− m| < M in |z| < 1, where |m−1| < M ≤ m. Recently, R.K. Pandey and G. P. Bhargava have shown that if f ε K (m,M), then the function du also belongs to K (m,M) provided α is a complex number satisfying the inequality |α| ≤ (1−b)/2, where b = (m-1)/M. In this paper we show by a counterexample that their inequality is in general wrong, and prove a corrected version of their result. We show that F ε K (m,M) provided that α is a real number satisfying −φ ≤ α ≤1, φ = (M−|m−1|)/(M + |m−1|), or a complex number satisfying |α| ≤ φ. In both cases the bounds for α are sharp.

scholarly journals NORM ESTIMATES OF THE PRE-SCHWARZIAN DERIVATIVES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS

2006 ◽  
Vol 49 (1) ◽  
pp. 131-143 ◽  
Author(s):  
Yong Chan Kim ◽  
Toshiyuki Sugawa
Keyword(s):  
Hardy Spaces ◽  
Convex Functions ◽  
Maximal Operator ◽  
Univalent Functions ◽  
Independent Interest ◽  
Norm Estimates ◽  
Norm Estimate ◽  
Schwarzian Derivatives ◽  
Derivatives Of

AbstractA sharp norm estimate will be given to the pre-Schwarzian derivatives of close-to-convex functions of specified type. In order to show the sharpness, we introduce a kind of maximal operator which may be of independent interest. We also discuss a relation between the subclasses of close-to-convex functions and the Hardy spaces.

scholarly journals The order of convexity for an integral operator

2016 ◽  
Vol 32 (1) ◽  
pp. 123-129
Author(s):  
VIRGIL PESCAR ◽  
◽  
CONSTANTIN LUCIAN ALDEA ◽  
◽  
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Order Of Convexity

In this paper we consider an integral operator for analytic functions in the open unit disk and we derive the order of convexity for this integral operator, on certain classes of univalent functions.

scholarly journals On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals Region of Variability for Exponentially Convex Univalent Functions

2010 ◽  
Vol 5 (3) ◽  
pp. 955-966 ◽  
Author(s):  
Ponnusamy Saminathan ◽  
Vasudevarao Allu ◽  
M. Vuorinen
Keyword(s):  
Univalent Functions ◽  
Convex Univalent Functions

scholarly journals Connections between Certain Subclasses of Analytic Univalent Functions Based on Operators

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
R. Ezhilarasi ◽  
T. V. Sudharsan ◽  
Maisarah Haji Mohd ◽  
K. G. Subramanian
Keyword(s):  
Linear Operator ◽  
Integral Operator ◽  
Hypergeometric Function ◽  
Analytic Functions ◽  
Univalent Functions

In this paper, by applying the Hohlov linear operator, connections between the class SD(α),  α≥0, and two subclasses of the class A of normalized analytic functions are established. Also an integral operator related to hypergeometric function is considered.

scholarly journals Applications of Certain Operators to the Classes of Analytic Functions Related to the Generalized Janowski Functions

2020 ◽  
pp. 211-225
Author(s):  
Khalida Inayat Noor ◽  
Shujaat Ali Shah
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Linear Operators ◽  
Janowski Functions ◽  
Radius Problems ◽  
Convex Univalent Functions

We introduce certain subclasses of analytic functions related to the class of analytic, convex univalent functions. We discuss some results including inclusion relationships and invariance of the classes under convex convolution in terms of certain linear operators. Applications of these results associated with the generalized Janowski functions and conic domains are considered. Also, several radius problems are investigated.

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