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THE SHARP BOUND FOR THE HANKEL DETERMINANT OF THE THIRD KIND FOR CONVEX FUNCTIONS

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0 Published in 2018 at "Bulletin of the Australian Mathematical Society"

DOI: 10.1017/s0004972717001125

Abstract: We prove the sharp inequality $|H_{3,1}(f)|\leq 4/135$ for convex functions, that is, for analytic functions $f$ with $a_{n}:=f^{(n)}(0)/n!,~n\in \mathbb{N}$ , such that $$\begin{eqnarray}Re\bigg\{1+\frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}\bigg\}>0\quad \text{for}~z\in \mathbb{D}:=\{z\in \mathbb{C}:|z| read more here.

Keywords: bound hankel; sharp bound; hankel determinant; convex functions ... See more keywords

THE THIRD HANKEL DETERMINANT FOR INVERSE COEFFICIENTS OF CONVEX FUNCTIONS

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1 Published in 2023 at "Bulletin of the Australian Mathematical Society"

DOI: 10.1017/s0004972723000357

Abstract: The sharp bound for the third Hankel determinant for the coefficients of the inverse function of convex functions is obtained, thus answering a recent conjecture concerning invariance of coefficient functionals for convex functions. read more here.

Keywords: third hankel; determinant inverse; hankel determinant; inverse coefficients ... See more keywords

Hankel determinant of order three for familiar subsets of analytic functions related with sine function

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0 Published in 2019 at "Open Mathematics"

DOI: 10.1515/math-2019-0132

Abstract: Abstract In this paper we define and consider some familiar subsets of analytic functions associated with sine functions in the region of unit disk on the complex plane. For these classes our aim is to… read more here.

Keywords: order three; familiar subsets; analytic functions; subsets analytic ... See more keywords

Sharp Bounds for the Second Hankel Determinant of Logarithmic Coefficients for Strongly Starlike and Strongly Convex Functions

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1 Published in 2022 at "Axioms"

DOI: 10.3390/axioms11080369

Abstract: The logarithmic coefficients are very essential in the problems of univalent functions theory. The importance of the logarithmic coefficients is due to the fact that the bounds on logarithmic coefficients of f can transfer to… read more here.

Keywords: logarithmic coefficients; bounds second; hankel determinant; sharp bounds ... See more keywords

A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain

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0 Published in 2019 at "Mathematics"

DOI: 10.3390/math7050418

Abstract: In the present article, we consider certain subfamilies of analytic functions connected with the cardioid domain in the region of the unit disk. The purpose of this article is to investigate the estimates of the… read more here.

Keywords: cardioid domain; third hankel; certain subfamilies; analytic functions ... See more keywords

Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions

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1 Published in 2019 at "Symmetry"

DOI: 10.3390/sym11030347

Abstract: The main purpose of this article is to find the upper bound of the third Hankel determinant for a family of q-starlike functions which are associated with the Ruscheweyh-type q-derivative operator. The work is motivated… read more here.

Keywords: starlike functions; upper bound; bound third; third hankel ... See more keywords

Fourth Hankel Determinant Problem Based on Certain Analytic Functions

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1 Published in 2022 at "Symmetry"

DOI: 10.3390/sym14040663

Abstract: : In recent years, the Hankel determinant bounds for different subclasses of analytic, starlike and symmetric starlike functions have been discussed and studied by the many well-known authors. In this paper, we first consider a… read more here.

Keywords: fourth hankel; based certain; determinant problem; hankel determinant ... See more keywords

Upper Bounds of the Third Hankel Determinant for Close-to-Convex Functions

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2 Published in 2022 at "Symmetry"

DOI: 10.3390/sym14050885

Abstract: In this paper, the third Hankel determinant for the class N of functions convex in one direction is estimated. An analogous problem is solved for a subclass of N consisting of functions with real coefficients.… read more here.

Keywords: upper bounds; third hankel; bounds third; hankel determinant ... See more keywords