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.

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.

On obtaining zero-free regions for the zeta-function from estimates of M(x)

1970 ◽  
Vol 67 (2) ◽  
pp. 333-337
Author(s):  
D. Allison
Keyword(s):  
Number Theory ◽  
Zeta Function ◽  
Analytic Number Theory ◽  
Möbius Function ◽  
Mobius Function ◽  
Analytic Number ◽  
Standard Notation

We use some of the standard notation of analytic number theory; ψ(x) is defined in (1), page 12, and where μ(n) is the Möbius function.

scholarly journals Some applications of the generalised Poisson-Jensen formula

1940 ◽  
Vol 6 (3) ◽  
pp. 151-156
Author(s):  
S. A. Scott
Keyword(s):  
Number Theory ◽  
Green’S Function ◽  
Zeta Function ◽  
Green's Function ◽  
Analytic Number Theory ◽  
General Function ◽  
Number Of Zeros ◽  
Analytic Number ◽  
Effective Use

The object of this paper is to show how some formulae in Analytic Number Theory, in particular, the formula for N(T), the number of zeros of the Zeta-function between t = 0 and t = T, are easy deductions from the Generalised Poisson-Jensen formula. A similar method, using Green's function instead of the general function g(s) of § 2, has been published by F. and R. Nevanlinna (Math. Zeitschrift, 20 (1924), and 23 (1925), but the result contained in (vi) below appears to be new, although the writer has not been able, as yet, to make any effective use of it. It is clear that other applications could be made, but it seems sufficient to give here an indication of the method. The notation throughout is the usual one, and the references are to the Cambridge Tract by E. C. Titchmarsh on “The Zeta-function of Riemann”. Finally, I am indebted to the referee for the reference to the papers of F. and R. Nevanlinna.

scholarly journals Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2539
Author(s):  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Hypergeometric Function ◽  
Complex Analysis ◽  
Function Theory ◽  
Confluent Hypergeometric Function ◽  
Differential Subordination ◽  
Geometric Function Theory ◽  
Geometric Function ◽  
Hypergeometric Integral ◽  
Differential Subordinations

This paper is related to notions adapted from fuzzy set theory to the field of complex analysis, namely fuzzy differential subordinations. Using the ideas specific to geometric function theory from the field of complex analysis, fuzzy differential subordination results are obtained using a new integral operator introduced in this paper using the well-known confluent hypergeometric function, also known as the Kummer hypergeometric function. The new hypergeometric integral operator is defined by choosing particular parameters, having as inspiration the operator studied by Miller, Mocanu and Reade in 1978. Theorems are stated and proved, which give corollary conditions such that the newly-defined integral operator is starlike, convex and close-to-convex, respectively. The example given at the end of the paper proves the applicability of the obtained results.

scholarly journals Mathematical Reminiscences: How to Keep the Pot Boiling

2013 ◽  
Vol Volume 34-35 ◽  
Author(s):  
K Ramachandra
Keyword(s):  
Number Theory ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Diophantine Equations ◽  
Analytic Number Theory ◽  
Transcendental Numbers ◽  
Analytic Number ◽  
The Riemann Zeta Function ◽  
International Audience ◽  
Riemann Zeta

International audience Analytic number theory deals with the application of analysis, both real and complex, to the study of numbers. It includes primes, transcendental numbers, diophantine equations and other questions. The study of the Riemann zeta-function $\zeta(s)$ is intimately connected with that of primes. \par In this note, edited specially for this volume by K. Srinivas, some problems from a handwritten manuscript of Ramachandra are listed.

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 Inclusion and convolution features of univalent meromorphic functions correlating with Mittag-Leffler function

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2141-2150
Author(s):  
F. Ghanim ◽  
Hiba Al-Janaby
Keyword(s):  
Applied Sciences ◽  
Integral Equations ◽  
Meromorphic Functions ◽  
Function Theory ◽  
Geometric Function Theory ◽  
Integrodifferential Operator ◽  
Geometric Function ◽  
Fractional Differential

The so-called Mittag-Leffler function (M-LF) provides solutions to the fractional differential or integral equations with numerous implementations in applied sciences and other allied disciplines. During the previous century, the interest in M-LF has significantly developed and a variety of extensions and generalizations forms of the M-LF have been posed. Moreover, M-LF played a distinguished and important role in Geometric Function Theory (GFT). The intent of the current study is to reveal various inclusion and convolution features for a specific subclass of univalent meromorphic functions correlating with the integrodifferential operator containing an extended generalized M-LF. Some consequences of the major geometric outcomes are also presented.

scholarly journals On Lie ideals and $ (\sigma, \tau)$-Jordan derivations An application of Briot-Bouquet differential subordination

2002 ◽  
Vol 33 (1) ◽  
pp. 1-12
Author(s):  
Jagannath Patel
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Function Theory ◽  
Differential Subordination ◽  
Open Unit ◽  
Geometric Function Theory ◽  
Open Unit Disc ◽  
Geometric Function

By using the method of Briot-Bouquet differential subordination, we prove and sharpen some classical results in geometric function theory. We also derive some criteria for univalency for certain classes analytic functions in the open unit disc.

Titchmarsh's theorem of Hankel transform

2019 ◽  
pp. 11-24
Author(s):  
Mohamed-Ahmed Boudref
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Analytic Number Theory ◽  
Hankel Transform ◽  
Partial Differential ◽  
Analytic Number ◽  
Bessel Transform

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

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