Sharp Estimates of the First Coefficients for a Class of Typically Real Functions

2016 ◽  
Vol 216 (6) ◽  
pp. 746-752
Author(s):  
E. G. Goluzina
Keyword(s):  
Sharp Estimates ◽  
Real Functions ◽  
Typically Real ◽  
Typically Real Functions

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

2018 ◽  
Vol 97 (2) ◽  
pp. 253-264 ◽  
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.

Coefficient inequalities related with typically real functions

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.

Coefficient Estimates of Some Classes of Analytic Functions

1983 ◽  
Vol 26 (2) ◽  
pp. 202-208
Author(s):  
Nicolas Samaris
Keyword(s):  
Analytic Functions ◽  
Positive Real Part ◽  
Coefficient Estimates ◽  
Positive Real ◽  
Real Functions ◽  
Typically Real ◽  
Typically Real Functions

AbstractWe are concerned with coefficient estimates, and other similar problems, of the typically real functions and of the functions with positive real part. Following the stream of ideas in [1], new results and generalizations of others given in [1], [2] and [3] are obtained.

On the Zalcman conjecture for starlike and typically real functions

1986 ◽  
Vol 191 (3) ◽  
pp. 467-474 ◽  
Author(s):  
Johnny E. Brown ◽  
Anna Tsao
Keyword(s):  
Real Functions ◽  
Typically Real ◽  
Typically Real Functions
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