scholarly journals Sufficient conditions for a certain general class of Carathéodory functions

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3615-3625 ◽  
Author(s):  
Qing-Hua Xu ◽  
Ting Yang ◽  
H.M. Srivastava
Keyword(s):  
Unit Disk ◽  
General Class ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Carathéodory Functions

In the present paper, the authors derive sufficient conditions for functions to be in a certain general class of Carath?odory functions in the open unit disk by using the Miller-Mocanu lemma. As an application of our main result, we deduce sufficient conditions for functions belonging to the class ST ?u? which is introduced here. The various results presented here would generalize and extend many known results.

scholarly journals Sufficient conditions for Carathéodory functions

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1097-1106 ◽  
Author(s):  
Mamoru Nunokawa ◽  
Oh Kwon ◽  
Young Sim ◽  
Nak Cho
Keyword(s):  
Unit Disk ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Carathéodory Functions ◽  
Special Cases

In the present paper, we obtain several sufficient conditions for Carath?odory functions in the open unit disk U = {z ? C : ?z? < 1}. We also obtain sufficient conditions for p-valent or starlike functions. Moreover, we improve some results due to Nunokawa [Tsukuba J. Math. 13 (1989), 453-455] as some special cases of main results.

scholarly journals Starlikeness of Functions Defined by Third-Order Differential Inequalities and Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
R. Chandrashekar ◽  
Rosihan M. Ali ◽  
K. G. Subramanian ◽  
A. Swaminathan
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Inequalities ◽  
Third Order ◽  
Positive Order

Sufficient conditions are obtained to ensure starlikeness of positive order for analytic functions defined in the open unit disk satisfying certain third-order differential inequalities. As a consequence, conditions for starlikeness of functions defined by integral operators are obtained. Connections are also made to earlier known results.

scholarly journals Some Connections between Class𝒰- andα-Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Edmond Aliaga ◽  
Nikola Tuneski
Keyword(s):  
Convex Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk

The class𝒰(λ,μ)of normalized analytic functions that satisfy|(z/f(z))1+μ·f′(z)−1|<λfor allzin the open unit disk is studied and sufficient conditions for anα-convex function to be in𝒰(λ,μ)are given.

scholarly journals Starlikeness and Convexity of Generalized Struve Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Nihat Yagmur ◽  
Halit Orhan
Keyword(s):  
Unit Disk ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Struve Functions

We give sufficient conditions for the parameters of the normalized form of the generalized Struve functions to be convex and starlike in the open unit disk.

scholarly journals Geometric Properties of a New Integral Operator

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Roberta Bucur ◽  
Loriana Andrei ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties ◽  
Special Cases

We obtain sufficient conditions for the univalence, starlikeness, and convexity of a new integral operator defined on the space of normalized analytic functions in the open unit disk. Some subordination results for the new integral operator are also given. Several corollaries follow as special cases.

scholarly journals On Univalence Criteria for a General Integral Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Vasile Marius Macarie ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Complex Plane ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
General Integral ◽  
General Integral Operator ◽  
Univalence Criteria

We consider a new general integral operator, and we give sufficient conditions for the univalence of this integral operator in the open unit disk of the complex plane. Several consequences of the main results are also shown.

scholarly journals Sharp coefficient estimates for a certain general class of Spirallike functions by means of differential subordination

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1351-1356 ◽  
Author(s):  
Qing-Hua Xu ◽  
Lv. Chun-Bo ◽  
Nan-Chen Luo ◽  
H.M. Srivastava
Keyword(s):  
Unit Disk ◽  
General Class ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sharp Estimates ◽  
Spirallike Functions

In the present paper, the authors derive several sharp estimates for the Taylor-Maclaurin coefficients of functions in a certain general class S?(A, B) of spirallike functions in the open unit disk U, which is defined here by using the principle of differential subordination The results presented here would generalize those given in the earlier work of R. J. Libera.

scholarly journals On q-ANALOGUE of Differential Subordination Associated with Lemniscate of Bernoulli

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mohsan Raza ◽  
Hira Naz ◽  
Sarfraz Nawaz Malik ◽  
Sahidul Islam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
Lemniscate Of Bernoulli

This article comprises the study of differential subordination with analogue of q -derivative. It includes the sufficient condition on γ for 1 + γ ∂ z q h z / h n z to be subordinated by 1 + A z / 1 + B z , − 1 ≤ B < A ≤ 1 , and implies that h z ≺ 1 + z , where h z is the analytic function in the open unit disk. Moreover, certain sufficient conditions for q -starlikeness of analytic functions related with lemniscate of Bernoulli are determined.

scholarly journals Properties of a new integral operator

2016 ◽  
Vol 24 (2) ◽  
pp. 127-136
Author(s):  
Roberta Bucur ◽  
Loriana Andrei ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk

Abstract In this paper, we derive sufficient conditions for the univalence, star- likeness, convexity and some other properties in the class N (ρ) ; for a new integral operator defined on the space of normalized analytic functions in the open unit disk.

SOME NEW RESULTS ASSOCIATED WITH CARATHÉODORY FUNCTIONS OF ORDER α

2016 ◽  
Vol 2 (1) ◽  
pp. 11-13
Author(s):  
H. M. Srivastava ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Extremal Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
Carathéodory Functions ◽  
Coefficient Inequalities ◽  
The Extremal Function ◽  
Class Of Functions

Let $\mathcal{P}(\alpha)$ be the class of functions $p(z)$ which are Carathéodory functions of order $\alpha$ $(0 \le\alpha<1)$ in the open unit disk $\mathbf{U}$. Considering the extremal function $p(z)$ for the class $\mathcal{P}(\alpha)$, a new class ${\mathcal P}^*(\beta)$ $\beta\in \mathbb{R}$ of functions $q(z)$ in $\mathbf{U}$ is defined. The object of the present paper is to develop several interesting coefficient inequalities for the functions $q(z)$ in the new class $\mathcal{P}^*(\beta)$ introduced here.

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