scholarly journals Differential Subordination Results for Analytic Functions in the Upper Half-Plane

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Huo Tang ◽  
M. K. Aouf ◽  
Guan-Tie Deng ◽  
Shu-Hai Li
Keyword(s):  
Unit Disk ◽  
Half Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Upper Half Plane ◽  
Admissible Functions

There are many articles in the literature dealing with differential subordination problems for analytic functions in the unit disk, and only a few articles deal with the above problems in the upper half-plane. In this paper, we aim to derive several differential subordination results for analytic functions in the upper half-plane by investigating certain suitable classes of admissible functions. Some useful consequences of our main results are also pointed out.

scholarly journals Fractional differential superordination

2014 ◽  
Vol 45 (3) ◽  
pp. 275-284
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Fractional Order ◽  
Analytic Functions ◽  
Dual Problem ◽  
Differential Subordination ◽  
Geometric Properties ◽  
Differential Superordination ◽  
Fractional Differential ◽  
Admissible Functions

The notion of differential superordination was introduced by S.S. Miller and P.T. Mocanu as a dual concept of differential subordination. Recently, in Tamkang J. Math.[7], the author have introduced the notion of fractional differential subordination. In this work, we consider the dual problem of determining properties of analytic functions that satisfy the fractional differential superordination. By employing some types of admissible functions, involving differential operator of fractional order, we illustrate geometric properties such as starlikeness and convexity for a class of analytic functions in the unit disk. Moreover, applications are posed in the sequel.

scholarly journals The concept of fractional differential subordination

2013 ◽  
Vol 44 (1) ◽  
pp. 53-60
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Fractional Order ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Fractional Operators ◽  
Geometric Properties ◽  
Fractional Differential ◽  
Admissible Functions

In this work, we consider a definition for the concept of fractional differential subordination in sense of Srivastava-Owa fractional operators. By employing some types of admissible functions, involving differential operator of fractional order, we illustrate geometric properties such as starlikeness and convexity for a class of analytic functions in the unit disk. Moreover, applications are posed in the sequel.

scholarly journals Differential subordination and superordination results for certain subclasses of analytic functions by the technique of admissible functions

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2009-2026
Author(s):  
R. Jayasankar ◽  
Maslina Darus ◽  
S. Sivasubramanian
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

By investigating appropriate classes of admissible functions, various Differential subordination and superordination results for analytic functions in the open unit disk are obtained using Cho-Kwon-Srivastava operator. As a consequence of these results, Sandwich-type results are also obtained.

scholarly journals Strong Differential Subordination Results for Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

2019 ◽  
pp. 159-168
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehdi
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Closed Unit Disk ◽  
Strong Differential Subordination

In this paper, by making use of the principle of strong subordination, we establish some interesting properties of multivalent analytic functions defined in the open unit disk and closed unit disk of the complex plane associated with Dziok-Srivastava operator.

scholarly journals On Sandwich Theorems Results for Certain Univalent Functions Defined by Generalized Operators

2021 ◽  
pp. 2376-2383
Author(s):  
Waggas Galib Atshan ◽  
Aqeel Ahmed Redha Ali
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Subordination And Superordination

In this present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results.

Some argument inequalities for certain analytic functions

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Jin-Lin Liu
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk

AbstractFor analytic functions f(z) in the open unit disk U and convex functions g(z) in U, Nunokawa et al. [NUNOKAWA, M.—OWA, S.—NISHIWAKI, J.—KUROKI, K.—HAYAMI, T: Differential subordination and argumental property, Comput. Math. Appl. 56 (2008), 2733–2736] have proved one theorem which is a generalization of the result [POMMERENKE, CH.: On close-toconvex analytic functions, Trans. Amer. Math. Soc. 114 (1965), 176–186]. The object of the present paper is to generalize the theorem due to Nunokawa et al..

scholarly journals Differential subordination and convexity criteria of integral operators

2017 ◽  
Vol 15 (1) ◽  
pp. 1509-1516
Author(s):  
R. Chandrashekar ◽  
See Keong Lee ◽  
K.G. Subramanian
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Integral Operators ◽  
Differential Subordination ◽  
Second Order ◽  
Fundamental Result ◽  
Open Unit ◽  
Open Unit Disk

Abstract A significant connection between certain second-order differential subordination and subordination of f′(z) is obtained. This fundamental result is next applied to investigate the convexity of analytic functions defined in the open unit disk. As a consequence, criteria for convexity of functions defined by integral operators are determined. Connections are also made to earlier known results.

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