Certain subclass of analytic functions II

Research output: Contribution to journalArticle

Abstract

Let f be analytic in D = {z : |z| < 1} with f(0) = f′(0) - 1 = 0 and f(z)/f(z) f′ (z) ≠ 0. Suppose δ ≥ 0 and γ > 0. For 0 < β < 1, the largest α(β, δ, γ) is found such that (δ(1+zf″(z)/f′(z)) + (γ-δ) (zf′(z)/f(z)) zf′(z)/f(z) ≺ (1+z/1-z) α(β,δ,γ) ⇒ zf′(z)/f(z) ≺ (1+z/1-z)β. The result solves the inclusion problem for certain subclass of analytic functions involving starlike and convex functions defined in a sector. Further we investigate the inclusion problem involving addition of powers of convex and starlike functions.

Original languageEnglish
Pages (from-to)127-134
Number of pages8
JournalActa Mathematica Academiae Paedagogicae Nyiregyhaziensis
Volume21
Issue number2
Publication statusPublished - 2005

Fingerprint

Starlike and Convex Functions
Analytic function
Inclusion
inclusion
Sector

Keywords

  • Convex function
  • Normalised
  • Starlike function
  • Univalent

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Certain subclass of analytic functions II. / Darus, Maslina.

In: Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, Vol. 21, No. 2, 2005, p. 127-134.

Research output: Contribution to journalArticle

@article{0be5cdbd8a154f4a9c66dcd20e64dc3e,
title = "Certain subclass of analytic functions II",
abstract = "Let f be analytic in D = {z : |z| < 1} with f(0) = f′(0) - 1 = 0 and f(z)/f(z) f′ (z) ≠ 0. Suppose δ ≥ 0 and γ > 0. For 0 < β < 1, the largest α(β, δ, γ) is found such that (δ(1+zf″(z)/f′(z)) + (γ-δ) (zf′(z)/f(z)) zf′(z)/f(z) ≺ (1+z/1-z) α(β,δ,γ) ⇒ zf′(z)/f(z) ≺ (1+z/1-z)β. The result solves the inclusion problem for certain subclass of analytic functions involving starlike and convex functions defined in a sector. Further we investigate the inclusion problem involving addition of powers of convex and starlike functions.",
keywords = "Convex function, Normalised, Starlike function, Univalent",
author = "Maslina Darus",
year = "2005",
language = "English",
volume = "21",
pages = "127--134",
journal = "Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis",
issn = "0866-0182",
publisher = "Nyregyhazi Foiskola/College of Nyregyhaza",
number = "2",

}

TY - JOUR

T1 - Certain subclass of analytic functions II

AU - Darus, Maslina

PY - 2005

Y1 - 2005

N2 - Let f be analytic in D = {z : |z| < 1} with f(0) = f′(0) - 1 = 0 and f(z)/f(z) f′ (z) ≠ 0. Suppose δ ≥ 0 and γ > 0. For 0 < β < 1, the largest α(β, δ, γ) is found such that (δ(1+zf″(z)/f′(z)) + (γ-δ) (zf′(z)/f(z)) zf′(z)/f(z) ≺ (1+z/1-z) α(β,δ,γ) ⇒ zf′(z)/f(z) ≺ (1+z/1-z)β. The result solves the inclusion problem for certain subclass of analytic functions involving starlike and convex functions defined in a sector. Further we investigate the inclusion problem involving addition of powers of convex and starlike functions.

AB - Let f be analytic in D = {z : |z| < 1} with f(0) = f′(0) - 1 = 0 and f(z)/f(z) f′ (z) ≠ 0. Suppose δ ≥ 0 and γ > 0. For 0 < β < 1, the largest α(β, δ, γ) is found such that (δ(1+zf″(z)/f′(z)) + (γ-δ) (zf′(z)/f(z)) zf′(z)/f(z) ≺ (1+z/1-z) α(β,δ,γ) ⇒ zf′(z)/f(z) ≺ (1+z/1-z)β. The result solves the inclusion problem for certain subclass of analytic functions involving starlike and convex functions defined in a sector. Further we investigate the inclusion problem involving addition of powers of convex and starlike functions.

KW - Convex function

KW - Normalised

KW - Starlike function

KW - Univalent

UR - http://www.scopus.com/inward/record.url?scp=24944505189&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944505189&partnerID=8YFLogxK

M3 - Article

VL - 21

SP - 127

EP - 134

JO - Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis

JF - Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis

SN - 0866-0182

IS - 2

ER -