scholarly journals Partial Sums of Certain Classes of Meromorphic Functions Related to the Hurwitz-Lerch Zeta Function

2015 ◽  
Vol 1 (1) ◽  
pp. 38-50 ◽  
Author(s):  
H. M. Srivastava ◽  
S. Gaboury ◽  
F. Ghanim
Keyword(s):  
Zeta Function ◽  
Unit Disk ◽  
Meromorphic Functions ◽  
Sufficient Conditions ◽  
Partial Sums ◽  
Its Sequence ◽  
Lerch Zeta Function

Abstract In the present paper, we give sufficient conditions for a function f to be in the subclasses ΣS*a,s (A. B, α, β) and ΣKa,s (A, B, α, β) of the class Σ of meromorphic functions which are analytic in the punctured unit disk U*. We further investigate the ratio of a function related to the Hurwitz-Lerch zeta function and its sequence of partial sums.

Certain classes of analytic functions defined by Hurwitz–Lerch zeta function

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Bolineni Venkateswarlu ◽  
Pinninti Thirupathi Reddy ◽  
Galla Swapna ◽  
Rompilli Madhuri Shilpa
Keyword(s):  
Zeta Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
New Class ◽  
Lerch Zeta Function

Abstract In this work, we introduce and investigate a new class k - U ⁢ S ~ s ⁢ ( b , μ , γ , t ) {k-\widetilde{US}_{s}(b,\mu,\gamma,t)} of analytic functions in the open unit disk U with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions f belonging to this class.

scholarly journals Partial Sums For Class Of Analytic Functions Defined By Integral Operator

2014 ◽  
Vol 8 (4) ◽  
Author(s):  
Nagat. M. Mustafa ◽  
Maslina Darus
Keyword(s):  
Integral Operator ◽  
Zeta Function ◽  
Analytic Functions ◽  
Partial Sums ◽  
Its Sequence ◽  
Coefficient Estimates ◽  
Lerch Zeta Function

In the present paper, we study the class of analytic functions involving generalized integral operator, which is defined by means of a general Hurwitz Lerch Zeta function denoted by ,()sbfzαℑwith negative coefficients. The aim of the paper is to obtain the coefficient estimates and also partial sums of its sequence ,()

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 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 Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Uma ◽  
M. Darus
Keyword(s):  
Analytic Function ◽  
Zeta Function ◽  
Lower Bounds ◽  
Analytic Functions ◽  
Partial Sums ◽  
Lerch Zeta Function

Letfn(z)=z+∑k=2nakzkbe the sequence of partial sums of the analytic functionf(z)=z+∑k=2∞akzk. In this paper, we determine sharp lower bounds forℜ{f(z)/fn(z)}, ℜ{fn(z)/f(z)}, ℜ{f′(z)/fn′(z)},andℜ{fn′(z)/f′(z)}. The usefulness of the main result not only provides the unification of the results discussed in the literature but also generates certain new results.

scholarly journals Sufficient conditions for meromorphic starlikeness and close-to-convexity of orderα

2001 ◽  
Vol 26 (5) ◽  
pp. 317-319 ◽  
Author(s):  
Nak Eun Cho ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Meromorphic Functions ◽  
Sufficient Conditions

The object of the present paper is to derive a property of certain meromorphic functions in the punctured unit disk. Our main theorem contains certain sufficient conditions for starlikeness and close-to-convexity of orderαof meromorphic functions.

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 Sufficient conditions for new integral transformation

2014 ◽  
Vol 8 (4) ◽  
Author(s):  
Aabed Mohammed ◽  
Maslina Darus
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Meromorphic Functions ◽  
Integral Transformation ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk

By using the integral transformation for meromorphic functions, an integral transformation on the class Aof analytic functions in the unit disk is defined. Some sufficient conditions for this transformation to be in the some known subclasses are derived. Furthermore, new function on the class of meromorphic functions in the punctured open unit disk is introduced. Finally, starlikeness conditions for this function are pointed out.

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