The growth of the derivative of a univalent function

1986 ◽  
pp. 143-152 ◽  
Author(s):  
Christian Pommerenke
Keyword(s):  
Univalent Function

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

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.

scholarly journals A truly isolated univalent function.

1980 ◽  
Vol 27 (2) ◽  
pp. 253-255
Author(s):  
Douglas M. Campbell
Keyword(s):  
Univalent Function

scholarly journals On Some Subclasses of $m$-fold Symmetric Bi-univalent Functions associated with the Sakaguchi Type Functions

2021 ◽  
pp. 1-15
Author(s):  
Ismaila O. Ibrahim ◽  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk

In the present investigation, we introduce the subclasses $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\phi,\upsilon)$ and $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\gamma,\upsilon)$ of $m$-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the Sakaguchi type of functions and defined in the open unit disk. Further, we obtain estimates on the initial coefficients $b_{m+1}$ and $b_{2m+1}$ for the functions of these subclasses and find out connections with some of the familiar classes.

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

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