On the computation of sets of points with low Lebesgue constant on the unit disk

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

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On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.35 ◽

2020 ◽

pp. 445-454

Author(s):

Deepali Khurana ◽

Sushma Gupta ◽

Sukhjit Singh

Keyword(s):

Present Article ◽

Unit Disk ◽

Imaginary Axis ◽

Harmonic Mappings ◽

Open Unit ◽

Open Unit Disk ◽

Distortion Bounds ◽

Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

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Coefficient inequalities related with typically real functions

Mathematica Slovaca ◽

10.1515/ms-2017-0396 ◽

2020 ◽

Vol 70 (4) ◽

pp. 829-838

Author(s):

Saqib Hussain ◽

Shahid Khan ◽

Khalida Inayat Noor ◽

Mohsan Raza

Keyword(s):

Unit Disk ◽

Real Functions ◽

Coefficient Inequalities ◽

Typically Real ◽

Class Of Functions ◽

Typically Real Functions

AbstractIn this paper, we are mainly interested to study the generalization of typically real functions in the unit disk. We study some coefficient inequalities concerning this class of functions. In particular, we find the Zalcman conjecture for generalized typically real functions.

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Some subordination involving polynomials induced by lower triangular matrices

Advances in Difference Equations ◽

10.1186/s13662-020-03002-3 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Saiful R. Mondal ◽

Kottakkaran Sooppy Nisar ◽

Thabet Abdeljawad

Keyword(s):

Unit Disk ◽

Triangular Matrices ◽

Cesàro Mean ◽

Cesaro Mean ◽

Lower Triangular ◽

Lower Triangular Matrices

Abstract The article considers several polynomials induced by admissible lower triangular matrices and studies their subordination properties. The concept generalizes the notion of stable functions in the unit disk. Several illustrative examples, including those related to the Cesàro mean, are discussed, and connections are made with earlier works.

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Radius problems for univalent functions

Journal of Applied Analysis ◽

10.1515/jaa-2020-2008 ◽

2020 ◽

Vol 26 (1) ◽

pp. 111-115

Author(s):

Janusz Sokół ◽

Katarzyna Trabka-Wiȩcław

Keyword(s):

Unit Disk ◽

Univalent Functions ◽

Radius Problems ◽

Radius Of Convexity

AbstractThis paper considers the following problem: for what value r, {r<1} a function that is univalent in the unit disk {|z|<1} and convex in the disk {|z|<r} becomes starlike in {|z|<1}. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.

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