scholarly journals Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huo Tang ◽  
H. M. Srivastava ◽  
Shu-Hai Li ◽  
Li-Na Ma
Keyword(s):  
Unit Disk ◽  
Differential Subordination ◽  
Convolution Operators ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Order Case ◽  
Differential Superordination ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

There are many articles in the literature dealing with the first-order and the second-order differential subordination and superordination problems for analytic functions in the unit disk, but only a few articles are dealing with the above problems in the third-order case (see, e.g., Antonino and Miller (2011) and Ponnusamy et al. (1992)). The concept of the third-order differential subordination in the unit disk was introduced by Antonino and Miller in (2011). Let Ω be a set in the complex planeC. Also letpbe analytic in the unit diskU=z:z∈C  and  z<1and suppose thatψ:C4×U→C. In this paper, we investigate the problem of determining properties of functionsp(z)that satisfy the following third-order differential superordination:Ω⊂ψpz,zp′z,z2p′′z,z3p′′′z;z:z∈U. As applications, we derive some third-order differential subordination and superordination results for meromorphically multivalent functions, which are defined by a family of convolution operators involving the Liu-Srivastava operator. The results are obtained by considering suitable classes of admissible functions.

scholarly journals Third-order differential subordination and superordination involving a fractional operator

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Muhammad Zaini Ahmad ◽  
Hiba F. Al-Janaby
Keyword(s):  
Fractional Integral ◽  
Differential Subordination ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Sandwich Type ◽  
Differential Superordination ◽  
Fractional Differential ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

AbstractThe third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.

scholarly journals An integrodifferential operator for meromorphic functions associated with the Hurwitz-Lerch zeta function

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 2045-2057 ◽  
Author(s):  
Adel Attiya ◽  
Sang Kwon ◽  
Park Hyang ◽  
Nak Cho
Keyword(s):  
Zeta Function ◽  
Meromorphic Functions ◽  
Differential Subordination ◽  
Open Disk ◽  
Third Order ◽  
The Third ◽  
Integrodifferential Operator ◽  
Lerch Zeta Function ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

In this paper, we introduce a new integrodifferential operator associated with the Hurwitz Lerch Zeta function in the puncture open disk of the meromorphic functions. We also obtain some properties of the third-order differential subordination and superordination for this integrodifferential operator, by using certain classes of admissible functions.

scholarly journals Applications of third order differential subordination and superordination involving generalized struve function

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3047-3059 ◽  
Author(s):  
Priyabrat Gochhayat ◽  
Anuja Prajapati
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Third Order ◽  
The Third ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Struve Functions ◽  
Differential Subordinations ◽  
Admissible Functions

In the present paper, by making use of the linear operator associated with generalized Struve functions suitable classes of admissible functions are investigated and the dual properties of the third-order differential subordinations are presented. As a consequence, various sandwich-type results are established for a class of univalent analytic functions involving generalized Struve functions. Relevant connections of the new results presented here with those that were considered in earlier works are pointed out.

scholarly journals Applications of differential subordinations involving a generalized fractional differintegral operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hanaa M. Zayed ◽  
Teodor Bulboacă
Keyword(s):  
Differential Subordination ◽  
Third Order ◽  
The Third ◽  
Fractional Differintegral ◽  
Differential Subordinations ◽  
Fractional Differintegral Operator ◽  
Admissible Functions

Abstract Using the third-order differential subordination basic results, we introduce certain classes of admissible functions and investigate some applications of third-order differential subordination for p-valent functions associated with generalized fractional differintegral operator.

scholarly journals On The Third-Order Complex Differential Inequalities of ξ-Generalized-Hurwitz–Lerch Zeta Functions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 845
Author(s):  
Hiba Al-Janaby ◽  
Firas Ghanim ◽  
Maslina Darus
Keyword(s):  
Differential Inequality ◽  
Function Theory ◽  
Zeta Functions ◽  
Differential Subordination ◽  
Geometric Function Theory ◽  
Third Order ◽  
The Third ◽  
Geometric Function ◽  
Z Domain ◽  
Admissible Functions

In the z- domain, differential subordination is a complex technique of geometric function theory based on the idea of differential inequality. It has formulas in terms of the first, second and third derivatives. In this study, we introduce some applications of the third-order differential subordination for a newly defined linear operator that includes ξ -Generalized-Hurwitz–Lerch Zeta functions (GHLZF). These outcomes are derived by investigating the appropriate classes of admissible functions.

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 Subordination and Superordination Results for Normalized Analytic Functions Associated with Frasin Operator

2019 ◽  
pp. 37-49
Author(s):  
Abbas Kareem Wanas ◽  
Sibel Yalçin
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
First Order ◽  
Differential Subordination And Superordination

In this paper, we derive some applications of first order differential subordination and superordination results involving Frasin operator for analytic functions in the open unit disk. Also by these results, we obtain sandwich results. Our results extend corresponding previously known results.

scholarly journals Differential Sandwich Theorems for a Certain Class of Analytic Functions Defined by Differential Operator

2019 ◽  
pp. 209-220
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehai
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
First Order ◽  
Differential Subordination And Superordination

In this paper, we establish some applications of first order differential subordination and superordination results involving Hadamard product for a certain class of analytic functions with differential operator defined in the open unit disk. These results are applied to obtain sandwich results.

scholarly journals Third-Order Differential Subordination Results for Analytic Functions Associated with a Certain Differential Operator

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 99
Author(s):  
Amal Mohammed Darweesh ◽  
Waggas Galib Atshan ◽  
Ali Hussein Battor ◽  
Alina Alb Lupaş
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Maclaurin Series ◽  
Third Order ◽  
Differential Superordination ◽  
Admissible Functions

In this research, we study suitable classes of admissible functions and establish the properties of third-order differential subordination by making use a certain differential operator of analytic functions in U and have the normalized Taylor–Maclaurin series of the form: f(z)=z+∑n=2∞anzn, (z∈U). Some new results on differential subordination with some corollaries are obtained. These properties and results are symmetry to the properties of the differential superordination to form the sandwich theorems.

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.

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