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 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 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 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 Certain Integral Operator Related to the Hurwitz–Lerch Zeta Function

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xiao-Yuan Wang ◽  
Lei Shi ◽  
Zhi-Ren Wang
Keyword(s):  
Integral Operator ◽  
Zeta Function ◽  
Meromorphic Functions ◽  
Third Order ◽  
Lerch Zeta Function ◽  
Sandwich Type ◽  
Differential Superordination ◽  
Differential Subordinations

The aim of the present paper is to investigate several third-order differential subordinations, differential superordination properties, and sandwich-type theorems of an integral operator Ws,bf(z) involving the Hurwitz–Lerch Zeta function. We make some applications of the operator Ws,bf(z) for meromorphic functions.

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 Differential Subordination Results for Certain Integrodifferential Operator and Its Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
M. A. Kutbi ◽  
A. A. Attiya
Keyword(s):  
Number Theory ◽  
Zeta Function ◽  
Function Theory ◽  
Analytic Number Theory ◽  
Differential Subordination ◽  
Geometric Function Theory ◽  
Integrodifferential Operator ◽  
Analytic Number ◽  
Geometric Function ◽  
Lerch Zeta Function

We introduce an integrodifferential operatorJs,b(f) which plays an important role in theGeometric Function Theory. Some theorems in differential subordination forJs,b(f) are used. Applications inAnalytic Number Theoryare also obtained which give new results for Hurwitz-Lerch Zeta function and Polylogarithmic function.

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