Sharp Estimates for the Coefficients of the Inverse Functions of the Nevanlinna Univalent Functions of the Classes N1 and N2

P. G. Todorov

doi:10.1007/bf02942553

Sharp Estimates for the Coefficients of the Inverse Functions of the Nevanlinna Univalent Functions of the Classes N1 and N2

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg ◽

10.1007/bf02942553 ◽

1998 ◽

Vol 68 (1) ◽

pp. 91-102

Author(s):

P. G. Todorov

Keyword(s):

Univalent Functions ◽

Sharp Estimates ◽

Inverse Functions

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Coefficient Inequalities of Functions Associated with Petal Type Domains

Mathematics ◽

10.3390/math6120298 ◽

2018 ◽

Vol 6 (12) ◽

pp. 298 ◽

Cited By ~ 1

Author(s):

Sarfraz Malik ◽

Shahid Mahmood ◽

Mohsan Raza ◽

Sumbal Farman ◽

Saira Zainab

Keyword(s):

Taylor Series ◽

Upper Bound ◽

Analytic Functions ◽

Univalent Functions ◽

Series Representation ◽

Functional Inequalities ◽

Major Interest ◽

Coefficient Inequalities ◽

Inverse Functions ◽

Analytic And Univalent Functions

In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains. One of the important and useful functional inequalities is the Fekete-Szegö inequality. In this work, we aim to analyze the Fekete-Szegö functional and to find its upper bound for certain analytic functions which give parabolic and petal type regions as image domains. Coefficient inequalities and the Fekete-Szegö inequality of inverse functions to these certain analytic functions are also established in this work.

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Hermitian Toeplitz determinants for the class S of univalent functions

Armenian Journal of Mathematics ◽

10.52737/18291163-2021.13.4-1-10 ◽

2021 ◽

pp. 1-10

Author(s):

Milutin Obradović ◽

Nikola Tuneski

Keyword(s):

Unit Disc ◽

Univalent Functions ◽

New Method ◽

Third Order ◽

Toeplitz Determinants ◽

New Approach ◽

Sharp Estimates

Introducing a new method, we give sharp estimates of the Hermitian Toeplitz determinants of third order for the class S of functions univalent in the unit disc. The new approach is also illustrated on some subclasses of the class S.

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TOEPLITZ DETERMINANTS WHOSE ELEMENTS ARE THE COEFFICIENTS OF ANALYTIC AND UNIVALENT FUNCTIONS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972717001174 ◽

2018 ◽

Vol 97 (2) ◽

pp. 253-264 ◽

Cited By ~ 6

Author(s):

MD FIROZ ALI ◽

D. K. THOMAS ◽

A. VASUDEVARAO

Keyword(s):

Univalent Functions ◽

Toeplitz Determinants ◽

Sharp Estimates ◽

Taylor Coefficients ◽

Real Functions ◽

Typically Real ◽

Analytic And Univalent Functions ◽

Typically Real Functions

Let ${\mathcal{S}}$ denote the class of analytic and univalent functions in $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ which are of the form $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$. We determine sharp estimates for the Toeplitz determinants whose elements are the Taylor coefficients of functions in ${\mathcal{S}}$ and certain of its subclasses. We also discuss similar problems for typically real functions.

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