scholarly journals Differential Subordination Results for Fractional Integral Associated with Generalized Mittag-Leffler Function

2019 ◽  
pp. 143-155
Author(s):  
Abbas Kareem Wanas ◽  
Alaa Hussein Khaleel
Keyword(s):  
Integral Representation ◽  
Unit Disk ◽  
Fractional Integral ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk

In this work, by making use of fractional integral, we define a certain class of holomorphic functions defined by generalized Mittag-Leffler function in the open unit disk U. Also, we establish some results for this class related to integral representation, inclusion relationship and argument estimate.

scholarly journals Differential Subordination Results for Holomorphic Functions Related to Differential Operator

2019 ◽  
Vol 11 (2) ◽  
pp. 46-53
Author(s):  
Abbas Kareem Wanas ◽  
S R Swamy
Keyword(s):  
Differential Operator ◽  
Integral Representation ◽  
Unit Disk ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties

,In the present work, we introduce and study a certain class of holomorphic functions defined by differential operator in the open unit disk . Also, we derive some important geometric properties for this class such as integral representation, inclusion relationship and argument estimate.

scholarly journals Differential Subordination Results for Holomorphic Functions Associated with Wanas Operator

2020 ◽  
pp. 249-261
Author(s):  
Abbas Kareem Wanas ◽  
Şahsene Altınkaya
Keyword(s):  
Integral Representation ◽  
Unit Disk ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties

In this investigation, we define a certain class of holomorphic functions defined by Wanas operator in the open unit disk U. We establish some important geometric properties for this class such as inclusion relationship, integral representation and argument estimate.

scholarly journals Some Subordination Results for Fractional Integral Involving Wanas Differential Operator

2020 ◽  
pp. 199-205
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Fractional Integral ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk

In the present paper, we establish some differential subordination properties for analytic functions defined in the open unit disk associated with the fractional integral by using Wanas differential operator.

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 A Property of the Principal Cluster sets of a Class of Holomorphic Functions

1971 ◽  
Vol 43 ◽  
pp. 157-159
Author(s):  
F. Bagemihl
Keyword(s):  
Meromorphic Function ◽  
Unit Circle ◽  
Unit Disk ◽  
Complex Plane ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Cluster Set ◽  
Principal Cluster

Let D be the open unit disk and Γ be the unit circle in the complex plane, and denote by Ω the Riemann sphere. If f(z) is a meromorphic function in D, and if ζ∈Г, then the principal cluster set of f at ζ is the set

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.

scholarly journals Weighted spaces of harmonic and holomorphic functions: sequence space representations and protective descriptions

1997 ◽  
Vol 40 (1) ◽  
pp. 41-62 ◽  
Author(s):  
Päivi Mattila ◽  
Eero Saksman ◽  
Jari Taskinen
Keyword(s):  
Unit Disk ◽  
Harmonic Functions ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Open Unit ◽  
Open Unit Disk ◽  
Inductive Limits ◽  
Complemented Subspaces ◽  
Bounded Functions ◽  
Köthe Sequence Spaces

We study the structure of inductive limits of weighted spaces of harmonic and holomorphic functions defined on the open unit disk of ℂ, and of the associated weighted locally convex spaces. Using a result of Lusky we prove, for certain radial weights on the open unit disk D of ℂ, that the spaces of harmonic and holomorphic functions are isomorphic to complemented subspaces of the corresponding Köthe sequence spaces. We also study the spaces of harmonic functions for certain non-radial weights on D. We show, under a natural sufficient condition for the weights, that the spaces of harmonic functions on D are isomorphic to corresponding spaces of continuous or bounded functions on ∂D.

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.

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