scholarly journals New Result of Analytic Functions Related to Hurwitz Zeta Function

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
F. Ghanim ◽  
M. Darus
Keyword(s):  
Analytic Function ◽  
Linear Operator ◽  
Zeta Function ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Hurwitz Zeta Function

By using a linear operator, we obtain some new results for a normalized analytic functionfdefined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed.

ON THE UNIVERSALITY OF THE HURWITZ ZETA-FUNCTION

2012 ◽  
Vol 09 (01) ◽  
pp. 155-165 ◽  
Author(s):  
ANTANAS LAURINČIKAS
Keyword(s):  
Analytic Function ◽  
Uniform Convergence ◽  
Zeta Function ◽  
Analytic Functions ◽  
Hurwitz Zeta Function ◽  
Space Of Analytic Functions ◽  
Rational Parameter ◽  
Compact Subsets

It is known that the Hurwitz zeta-function ζ(s, α) with transcendental or rational parameter α is universal in the sense that its shifts ζ(s + iτ, α), τ ∈ ℝ, approximate with a given accuracy any analytic function uniformly on compact subsets of the strip D = {s ∈ ℂ : ½ < σ < 1}. Let H(D) denote the space of analytic functions on D equipped with the topology of uniform convergence on compacta. In the paper, the classes of functions F : H(D) → H(D) such that F(ζ(s, α)) is universal in the above sense are considered. For example, if F is continuous and, for each polynomial p = p(s), the set F-1{p} is non-empty, then F(ζ(s, α)) with transcendental α is universal.

scholarly journals ON APPROXIMATION OF ANALYTIC FUNCTIONS BY PERIODIC HURWITZ ZETA-FUNCTIONS

2018 ◽  
Vol 24 (1) ◽  
pp. 20-33 ◽  
Author(s):  
Darius Siaučiūnas ◽  
Violeta Franckevič ◽  
Antanas Laurinčikas
Keyword(s):  
Zeta Function ◽  
Complex Plane ◽  
Analytic Functions ◽  
Zeta Functions ◽  
Periodic Sequence ◽  
Hurwitz Zeta Function ◽  
Complex Numbers ◽  
Closed Set

The periodic Hurwitz zeta-function ζ(s, α; a), s = σ +it, with parameter 0 < α ≤ 1 and periodic sequence of complex numbers a = {am } is defined, for σ > 1, by series sum from m=0 to ∞ am / (m+α)s, and can be continued moromorphically to the whole complex plane. It is known that the function ζ(s, α; a) with transcendental orrational α is universal, i.e., its shifts ζ(s + iτ, α; a) approximate all analytic functions defined in the strip D = { s ∈ C : 1/2 σ < 1. In the paper, it is proved that, for all 0 < α ≤ 1 and a, there exists a non-empty closed set Fα,a of analytic functions on D such that every function f ∈ Fα,a can be approximated by shifts ζ(s + iτ, α; a).

scholarly journals Inclusion Properties for Certain Subclasses of Analytic Functions Defined by a Linear Operator

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Nak Eun Cho
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Linear Operators ◽  
Inclusion Properties

The purpose of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions associated with a family of linear operators, which are defined by means of the Hadamard product (or convolution). Some integral preserving properties are also considered.

scholarly journals ON DISCRETE UNIVERSALITY OF COMPOSITE FUNCTIONS

2012 ◽  
Vol 17 (2) ◽  
pp. 271-280 ◽  
Author(s):  
Jovita Rašytė
Keyword(s):  
Analytic Function ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Space Of Analytic Functions ◽  
Composite Functions ◽  
The Riemann Zeta Function ◽  
Fixed Positive Number ◽  
Riemann Zeta ◽  
Discrete Universality

In 1975, S.M. Voronin proved that the Riemann zeta-function ζ (s) is universal in the sense that its shifts approximate uniformly on some sets any analytic function. Let h be a fixed positive number such that exp is irrational for all . In the paper, the classes of functions F such that the shifts F (ζ (s + imh)), , approximate any analytic function are presented. For the proof of theorems, some elements of the space of analytic functions are applied.

scholarly journals Subordination Results for a Class of Analytic Functions Defined by Convolution

2020 ◽  
pp. 137-143
Author(s):  
E. A. Adwan
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Paper Making ◽  
New Class ◽  
Special Cases

Aims/ Objectives: In this paper, making use the Hadamard product , we introduce drive several interesting subordination results for a new class of analytic function. Furthermore, we mention some known and new results, which follow as special cases of our results.

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 Some results on certain subclasses of analytic functions involving generalized hypergeometric functions and Hadamard product

1992 ◽  
Vol 15 (1) ◽  
pp. 143-148
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Hadamard Product ◽  
Generalized Hypergeometric Functions ◽  
Hypergeometric Type

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disc are introduced and some unifying relationships between them are established. A variety of characterization results involving a certain functional and some general functions of hypergeometric type are investigated for these classes.

scholarly journals Properties of some families of meromorphic multivalent functions involving certain linear operator

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 35-54 ◽  
Author(s):  
M.K. Aouf ◽  
B.A. Frasin
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Hadamard Products ◽  
Class A

Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce two novel subclasses ?a,c (p, A, B, ?) and ?+a,c (p, A, B, ?) of meromorphically multivalent functions. The main object of this paper is to investigate the various important properties and characteristics of those subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions. We also derive many results for the Hadamard products of functions belonging to the class ?+a,c (p, ?, ?, ?, ?).

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