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 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 Certain new subclasses of \(m\)-fold symmetric bi-pseudo-starlike functions using \(Q\)-derivative operator

2021 ◽  
Vol 5 (1) ◽  
pp. 42-50
Author(s):  
Timilehin Gideon Shaba ◽  
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Holomorphic Functions ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Special Cases

In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.

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 Simple sufficient conditions for starlikeness and convexity for meromorphic functions

2016 ◽  
Vol 14 (1) ◽  
pp. 557-566
Author(s):  
Pranay Goswami ◽  
Teodor Bulboacă ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Unit Disk ◽  
Meromorphic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases ◽  
Convexity Conditions

AbstractIn this paper we investigate some extensions of sufficient conditions for meromorphic multivalent functions in the open unit disk to be meromorphic multivalent starlike and convex of order α. Our results unify and extend some starlikeness and convexity conditions for meromorphic multivalent functions obtained by Xu et al. [2], and some interesting special cases are given.

scholarly journals A Subclass of q-Starlike Functions Defined by Using a Symmetric q-Derivative Operator and Related with Generalized Symmetric Conic Domains

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 917
Author(s):  
Shahid Khan ◽  
Saqib Hussain ◽  
Muhammad Naeem ◽  
Maslina Darus ◽  
Akhter Rasheed
Keyword(s):  
Unit Disk ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Necessary And Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivative Operator ◽  
Structural Formulas ◽  
Necessary And Sufficient

In this paper, the concepts of symmetric q-calculus and conic regions are used to define a new domain Ωk,q,α˜, which generalizes the symmetric conic domains. By using the domain Ωk,q,α˜, we define a new subclass of analytic and q-starlike functions in the open unit disk U and establish some new results for functions of this class. We also investigate a number of useful properties and characteristics of this subclass, such as coefficients estimates, structural formulas, distortion inequalities, necessary and sufficient conditions, closure and subordination results. The proposed approach is also compared with some existing methods to show the reliability and effectiveness of the proposed methods.

scholarly journals Sufficiency Criteria for q -Starlike Functions Associated with Cardioid

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Saira Zainab ◽  
Ayesha Shakeel ◽  
Muhammad Imran ◽  
Nazeer Muhammad ◽  
Hira Naz ◽  
...  
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Image Domain ◽  
Lemniscate Of Bernoulli ◽  
Differential Subordinations

This article deals with the q -differential subordinations for starlike functions associated with the lemniscate of Bernoulli and cardioid domain. The primary goal of this work is to find the conditions on γ for 1 + γ z ∂ q   h z / h n   z   ≺ 1 + z , where h z is analytic function and is subordinated by the function which is producing cardioid domain as its image domain while mapping the open unit disk. Along with this, certain sufficient conditions for q -starlikeness of analytic functions are determined.

scholarly journals On the Fekete-Szegö problem

2000 ◽  
Vol 24 (9) ◽  
pp. 577-581 ◽  
Author(s):  
B. A. Frasin ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Upper Bound ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Strongly Starlike Functions ◽  
Strongly Starlike

Letf(z)=z+a2z2+a3z3+⋯be an analytic function in the open unit disk. A sharp upper bound is obtained for|a3−μa22|by using the classes of strongly starlike functions of orderβand typeαwhenμ≥1.

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

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 Hankel and Toeplitz Determinants for a Subclass of q-Starlike Functions Associated with a General Conic Domain

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 181 ◽  
Author(s):  
Hari Srivastava ◽  
Qazi Ahmad ◽  
Nasir Khan ◽  
Nazar Khan ◽  
Bilal Khan
Keyword(s):  
Unit Disk ◽  
Toeplitz Matrices ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Toeplitz Determinants ◽  
Conic Domain

By using a certain general conic domain as well as the quantum (or q-) calculus, here we define and investigate a new subclass of normalized analytic and starlike functions in the open unit disk U . In particular, we find the Hankel determinant and the Toeplitz matrices for this newly-defined class of analytic q-starlike functions. We also highlight some known consequences of our main results.

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