The Schwarz Inequality and the Schwarz Formula for A-Analytic Functions

2018 ◽  
Vol 64 (4) ◽  
pp. 637-649
Author(s):  
N M Zhabborov ◽  
T U Otaboev ◽  
Sh Ya Khursanov
Keyword(s):  
Analytic Functions ◽  
Schwarz Inequality ◽  
Poisson Formula ◽  
Fundamental Theorems ◽  
Schwarz Formula

In this paper, we study A-analytic functions. We consider main fundamental theorems of the theory of A-analytic functions and prove analogs of the Schwarz inequality, the Schwars formula, and the Poisson formula for A-analytic functions.

scholarly journals An improved Schwarz Lemma at the boundary

2018 ◽  
Vol 16 (1) ◽  
pp. 1140-1144
Author(s):  
Peter R. Mercer
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Schwarz Inequality ◽  
Schwarz Lemma

AbstractWe obtain an new boundary Schwarz inequality, for analytic functions mapping the unit disk to itself. The result contains and improves a number of known estimates.

On characteristic of bounded analytic functions involving hyperbolic derivative

2018 ◽  
Vol 68 (4) ◽  
pp. 811-822
Author(s):  
Nan Wu
Keyword(s):  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Hyperbolic Derivative ◽  
Continuous Work ◽  
Angular Domains ◽  
Simply Connected ◽  
Fundamental Theorems ◽  
First Time ◽  
Simply Connected Domains

Abstract In this article, we give the Nevanlinna type hyperbolic characteristics in simply connected domains and angular domains and the Tsuji type hyperbolic characteristics for bounded analytic functions for the first time. The first fundamental theorems are also established concerning hyperbolic derivative for bounded analytic functions in simply connected domains and angular domains. This is a continuous work of Makhmutov [3].

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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