Coefficient inequality for a function whose derivative has a positive real part of order $\alpha$

Krishna, Deekonda Vamshee, and Ramreddy, Thoutreddy. "Coefficient inequality for a function whose derivative has a positive real part of order $\alpha $." Mathematica Bohemica 140.1 (2015): 43-52. <http://eudml.org/doc/269873>.

@article{Krishna2015,
abstract = {The objective of this paper is to obtain sharp upper bound for the function $f$ for the second Hankel determinant $|a_\{2\}a_\{4\}-a_\{3\}^\{2\}|$, when it belongs to the class of functions whose derivative has a positive real part of order $\alpha $$(0\le \alpha <1)$, denoted by $ RT(\alpha )$. Further, an upper bound for the inverse function of $f$ for the nonlinear functional (also called the second Hankel functional), denoted by $|t_\{2\}t_\{4\}-t_\{3\}^\{2\}|$, was determined when it belongs to the same class of functions, using Toeplitz determinants.},
author = {Krishna, Deekonda Vamshee, Ramreddy, Thoutreddy},
journal = {Mathematica Bohemica},
keywords = {analytic function; upper bound; second Hankel functional; positive real function; Toeplitz determinant},
language = {eng},
number = {1},
pages = {43-52},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Coefficient inequality for a function whose derivative has a positive real part of order $\alpha $},
url = {http://eudml.org/doc/269873},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Krishna, Deekonda Vamshee
AU - Ramreddy, Thoutreddy
TI - Coefficient inequality for a function whose derivative has a positive real part of order $\alpha $
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 1
SP - 43
EP - 52
AB - The objective of this paper is to obtain sharp upper bound for the function $f$ for the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$, when it belongs to the class of functions whose derivative has a positive real part of order $\alpha $$(0\le \alpha <1)$, denoted by $ RT(\alpha )$. Further, an upper bound for the inverse function of $f$ for the nonlinear functional (also called the second Hankel functional), denoted by $|t_{2}t_{4}-t_{3}^{2}|$, was determined when it belongs to the same class of functions, using Toeplitz determinants.
LA - eng
KW - analytic function; upper bound; second Hankel functional; positive real function; Toeplitz determinant
UR - http://eudml.org/doc/269873
ER -