Application of the Cauchy theorem to the location of zeros of sectionally analytic functions

1984 ◽  
Vol 35 (5) ◽  
pp. 705-711 ◽  
Author(s):  
E. G. Anastasselou ◽  
N. I. Ioakimidis
Keyword(s):  
Analytic Functions ◽  
Cauchy Theorem ◽  
Location Of Zeros

scholarly journals On the regions containing all the zeros of polynomials and related analytic functions

2021 ◽  
Vol 8 (2) ◽  
pp. 331-337
Author(s):  
Nisar Ahmad Rather ◽  
◽  
Ishfaq Dar ◽  
Aaqib Iqbal ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Zeros Of Polynomials ◽  
Location Of Zeros ◽  
Standard Techniques

In this paper, by using standard techniques we shall obtain results with relaxed hypothesis which give zero bounds for the larger class of polynomials. Our results not only generalizes several well-known results but also provide better information about the location of zeros. We also obtain a similar result for analytic functions. In addition to this, we show by examples that our result gives better information on the zero bounds of polynomials than some known results.

scholarly journals Functional Dependence and Analytic Functions

1979 ◽  
Vol 22 (3) ◽  
pp. 367-369
Author(s):  
P. Ramankutty
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Function Theory ◽  
Functional Dependence ◽  
Complex Variables ◽  
Several Complex Variables ◽  
The Real ◽  
Cauchy Theorem ◽  
Complex Valued ◽  
Constant Complex

AbstractWithout appealing to the Cauchy theorem or its corollaries, it is proved that the real and imaginary parts of a non-constant complex-valued analytic function of several complex variables are functionally independent. This unifies and generalizes some results sporadically treated in standard treatises on function theory.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions
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