Radius estimates of a subclass of univalent functions

Maslina Darus, Rabha W. Ibrahim

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

For analytic functions f normalized by f(0) = f0'(0) - 1 = 0 in the open unit disk U, a class Pα(λ) of f{hook} defined by{pipe}Dα z(z/f{hook}(z)){pipe} ≤, where Dα z denotes the fractional derivative of order α, m ≤ α < m + 1, m ε N0, is introduced. In this article, we study the problem when 1/r f{hook}(rz) ε Pα(λ), 3 ≤ α < 4.

Original languageEnglish
Pages (from-to)55-58
Number of pages4
JournalMatematicki Vesnik
Volume63
Issue number1
Publication statusPublished - 2011

Fingerprint

Univalent Functions
Fractional Derivative
Unit Disk
Analytic function
Radius
Denote
Estimate
Class

Keywords

  • Analytic functions
  • Cauchy-Schwarz inequality
  • Fractional differential operator
  • Univalent functions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Radius estimates of a subclass of univalent functions. / Darus, Maslina; Ibrahim, Rabha W.

In: Matematicki Vesnik, Vol. 63, No. 1, 2011, p. 55-58.

Research output: Contribution to journalArticle

Darus, M & Ibrahim, RW 2011, 'Radius estimates of a subclass of univalent functions', Matematicki Vesnik, vol. 63, no. 1, pp. 55-58.
Darus, Maslina ; Ibrahim, Rabha W. / Radius estimates of a subclass of univalent functions. In: Matematicki Vesnik. 2011 ; Vol. 63, No. 1. pp. 55-58.
@article{8d50dfe01fb94d18bd74f9bd54d2a9ad,
title = "Radius estimates of a subclass of univalent functions",
abstract = "For analytic functions f normalized by f(0) = f0'(0) - 1 = 0 in the open unit disk U, a class Pα(λ) of f{hook} defined by{pipe}Dα z(z/f{hook}(z)){pipe} ≤, where Dα z denotes the fractional derivative of order α, m ≤ α < m + 1, m ε N0, is introduced. In this article, we study the problem when 1/r f{hook}(rz) ε Pα(λ), 3 ≤ α < 4.",
keywords = "Analytic functions, Cauchy-Schwarz inequality, Fractional differential operator, Univalent functions",
author = "Maslina Darus and Ibrahim, {Rabha W.}",
year = "2011",
language = "English",
volume = "63",
pages = "55--58",
journal = "Matematicki Vesnik",
issn = "0025-5165",
publisher = "Drustvo Matematicara Srbije",
number = "1",

}

TY - JOUR

T1 - Radius estimates of a subclass of univalent functions

AU - Darus, Maslina

AU - Ibrahim, Rabha W.

PY - 2011

Y1 - 2011

N2 - For analytic functions f normalized by f(0) = f0'(0) - 1 = 0 in the open unit disk U, a class Pα(λ) of f{hook} defined by{pipe}Dα z(z/f{hook}(z)){pipe} ≤, where Dα z denotes the fractional derivative of order α, m ≤ α < m + 1, m ε N0, is introduced. In this article, we study the problem when 1/r f{hook}(rz) ε Pα(λ), 3 ≤ α < 4.

AB - For analytic functions f normalized by f(0) = f0'(0) - 1 = 0 in the open unit disk U, a class Pα(λ) of f{hook} defined by{pipe}Dα z(z/f{hook}(z)){pipe} ≤, where Dα z denotes the fractional derivative of order α, m ≤ α < m + 1, m ε N0, is introduced. In this article, we study the problem when 1/r f{hook}(rz) ε Pα(λ), 3 ≤ α < 4.

KW - Analytic functions

KW - Cauchy-Schwarz inequality

KW - Fractional differential operator

KW - Univalent functions

UR - http://www.scopus.com/inward/record.url?scp=78650612236&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650612236&partnerID=8YFLogxK

M3 - Article

VL - 63

SP - 55

EP - 58

JO - Matematicki Vesnik

JF - Matematicki Vesnik

SN - 0025-5165

IS - 1

ER -