scholarly journals The Bohr phenomenon for analytic functions on shifted disks

2021 ◽  
Vol 47 (1) ◽  
pp. 103-120
Author(s):  
Molla Basir Ahamed ◽  
Vasudevarao Allu ◽  
Himadri Halder
Keyword(s):  
Connected Domain ◽  
Analytic Functions ◽  
Bohr Radius ◽  
Simply Connected Domain ◽  
Simply Connected

In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain \(\Omega_{\gamma}=\bigg\{z\in\mathbb{C} \colon \bigg|z+\frac{\gamma}{1-\gamma}\bigg|<\frac{1}{1-\gamma}\bigg\}\) for \(0\leq \gamma<1.\) We study improved Bohr radius, Bohr-Rogosinski radius and refined Bohr radius for the class of analytic functions defined in \(\Omega_{\gamma}\), and obtain several sharp results.

scholarly journals Ideal Convergence ofk-Positive Linear Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Akif Gadjiev ◽  
Oktay Duman ◽  
A. M. Ghorbanalizadeh
Keyword(s):  
Complex Plane ◽  
Connected Domain ◽  
Analytic Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Ideal Convergence ◽  
Simply Connected Domain ◽  
Convergence Results ◽  
Simply Connected

We study some ideal convergence results ofk-positive linear operators defined on an appropriate subspace of the space of all analytic functions on a bounded simply connected domain in the complex plane. We also show that our approximation results with respect to ideal convergence are more general than the classical ones.

scholarly journals On ideal convergence of sequences of linear operators in the space of analytic functions

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 241-251
Author(s):  
Nursel Çetin
Keyword(s):  
Complex Plane ◽  
Connected Domain ◽  
Analytic Functions ◽  
Linear Operators ◽  
Space Of Analytic Functions ◽  
Ideal Convergence ◽  
Simply Connected Domain ◽  
Convergence Of Sequences ◽  
Simply Connected

We investigate the problem of ideal convergence of the sequences of linear operators without the properties of k-positivity in the space of analytic functions in a bounded simply connected domain of complex plane.

scholarly journals Approximation of analytic functions by sequences of linear operators

Filomat ◽  
2014 ◽  
Vol 28 (1) ◽  
pp. 99-106 ◽  
Author(s):  
Akif Gadjiev ◽  
Nursel Çetіn
Keyword(s):  
Connected Domain ◽  
Analytic Functions ◽  
Linear Operators ◽  
Simply Connected Domain ◽  
Simply Connected

In the present paper, we investigate approximation of analytic functions and their derivatives in a bounded simply connected domain by the sequences of linear operators without the properties of k?positivity.

scholarly journals A version of Runge's theorem for the Helmholtz equation with applications to scattering theory

1989 ◽  
Vol 32 (1) ◽  
pp. 107-119 ◽  
Author(s):  
R. L. Ochs
Keyword(s):  
Wave Function ◽  
Helmholtz Equation ◽  
Connected Domain ◽  
Scattering Theory ◽  
Polar Coordinates ◽  
Differentiable Functions ◽  
Simply Connected Domain ◽  
Image Position ◽  
Simply Connected

Let D be a bounded, simply connected domain in the plane R2 that is starlike with respect to the origin and has C2, α boundary, ∂D, described by the equation in polar coordinateswhere C2, α denotes the space of twice Hölder continuously differentiable functions of index α. In this paper, it is shown that any solution of the Helmholtz equationin D can be approximated in the space by an entire Herglotz wave functionwith kernel g ∈ L2[0,2π] having support in an interval [0, η] with η chosen arbitrarily in 0 > η < 2π.

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