The second hankel determinant of functions convex in one direction

D. K. Thomas

doi:10.12988/ijma.2016.619

The second hankel determinant of functions convex in one direction

Marjono
, D. K. Thomas

Faculty of Mathematics and Natural Sciences

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

It is shown that if f is analytic in z ∈ D = (z: |z| < 1) with f(z) = z + Σ^∞_n=2 a_nzⁿ, and is convex in one direction, then the second Hankel determinant H₂(2) = |a₂a₄ - a²₃| ≤ 1. The inequality is sharp.

Original language	English
Pages (from-to)	423-428
Number of pages	6
Journal	International Journal of Mathematical Analysis
Volume	10
Issue number	9-12
DOIs	https://doi.org/10.12988/ijma.2016.619
Publication status	Published - 2016

Keywords

Close-to-convex
Hankel determinants
Koebe function
Starlike
Univalent functions

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title = "The second hankel determinant of functions convex in one direction",

abstract = "It is shown that if f is analytic in z ∈ D = (z: |z| < 1) with f(z) = z + Σ∞n=2 anzn, and is convex in one direction, then the second Hankel determinant H2(2) = |a2a4 - a23| ≤ 1. The inequality is sharp.",

keywords = "Close-to-convex, Hankel determinants, Koebe function, Starlike, Univalent functions",

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year = "2016",

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T1 - The second hankel determinant of functions convex in one direction

AU - Marjono,

AU - Thomas, D. K.

PY - 2016

Y1 - 2016

N2 - It is shown that if f is analytic in z ∈ D = (z: |z| < 1) with f(z) = z + Σ∞n=2 anzn, and is convex in one direction, then the second Hankel determinant H2(2) = |a2a4 - a23| ≤ 1. The inequality is sharp.

AB - It is shown that if f is analytic in z ∈ D = (z: |z| < 1) with f(z) = z + Σ∞n=2 anzn, and is convex in one direction, then the second Hankel determinant H2(2) = |a2a4 - a23| ≤ 1. The inequality is sharp.

KW - Close-to-convex

KW - Hankel determinants

KW - Koebe function

KW - Starlike

KW - Univalent functions

UR - https://www.scopus.com/pages/publications/84973556231

U2 - 10.12988/ijma.2016.619

DO - 10.12988/ijma.2016.619

M3 - Article

AN - SCOPUS:84973556231

SN - 1312-8876

VL - 10

SP - 423

EP - 428

JO - International Journal of Mathematical Analysis

JF - International Journal of Mathematical Analysis

IS - 9-12

ER -

The second hankel determinant of functions convex in one direction

Abstract

Keywords

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