On subclasses for generalized operators of complex order

Maslina Darus, Rabha W. Ibrahim

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We define generalized differential and integral operators on the class A of analytic functions f(z) = z + Σ n=2 a nzn in the unit disk U := {z ε ℂ : | z | < 1} involving k-th Hadamard product (convolution) as follows: Dk α,β,λ,f(z) = z + Σ n=2[β(n-1)(λ-α) + 1]kanz n, (zεU). These operators are the generalized form of some well-known operators, for example, Sǎlǎgean operator and Al-Oboudi operator. New classes containing these operators of complex order are investigated.

Original languageEnglish
Pages (from-to)299-308
Number of pages10
JournalFar East Journal of Mathematical Sciences
Volume33
Issue number3
Publication statusPublished - Jun 2009

Fingerprint

Operator
Hadamard Product
Integral Operator
Unit Disk
Differential operator
Convolution
Analytic function
Class
Form

Keywords

  • Al-Oboudi operator
  • Differential operator
  • Hadamard product
  • Integral operator
  • Salagean operator

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On subclasses for generalized operators of complex order. / Darus, Maslina; Ibrahim, Rabha W.

In: Far East Journal of Mathematical Sciences, Vol. 33, No. 3, 06.2009, p. 299-308.

Research output: Contribution to journalArticle

@article{091452b8883a45019653b2a55df6a117,
title = "On subclasses for generalized operators of complex order",
abstract = "We define generalized differential and integral operators on the class A of analytic functions f(z) = z + Σ∞ n=2 a nzn in the unit disk U := {z ε ℂ : | z | < 1} involving k-th Hadamard product (convolution) as follows: Dk α,β,λ,f(z) = z + Σ∞ n=2[β(n-1)(λ-α) + 1]kanz n, (zεU). These operators are the generalized form of some well-known operators, for example, Sǎlǎgean operator and Al-Oboudi operator. New classes containing these operators of complex order are investigated.",
keywords = "Al-Oboudi operator, Differential operator, Hadamard product, Integral operator, Salagean operator",
author = "Maslina Darus and Ibrahim, {Rabha W.}",
year = "2009",
month = "6",
language = "English",
volume = "33",
pages = "299--308",
journal = "Far East Journal of Mathematical Sciences",
issn = "0972-0871",
publisher = "University of Allahabad",
number = "3",

}

TY - JOUR

T1 - On subclasses for generalized operators of complex order

AU - Darus, Maslina

AU - Ibrahim, Rabha W.

PY - 2009/6

Y1 - 2009/6

N2 - We define generalized differential and integral operators on the class A of analytic functions f(z) = z + Σ∞ n=2 a nzn in the unit disk U := {z ε ℂ : | z | < 1} involving k-th Hadamard product (convolution) as follows: Dk α,β,λ,f(z) = z + Σ∞ n=2[β(n-1)(λ-α) + 1]kanz n, (zεU). These operators are the generalized form of some well-known operators, for example, Sǎlǎgean operator and Al-Oboudi operator. New classes containing these operators of complex order are investigated.

AB - We define generalized differential and integral operators on the class A of analytic functions f(z) = z + Σ∞ n=2 a nzn in the unit disk U := {z ε ℂ : | z | < 1} involving k-th Hadamard product (convolution) as follows: Dk α,β,λ,f(z) = z + Σ∞ n=2[β(n-1)(λ-α) + 1]kanz n, (zεU). These operators are the generalized form of some well-known operators, for example, Sǎlǎgean operator and Al-Oboudi operator. New classes containing these operators of complex order are investigated.

KW - Al-Oboudi operator

KW - Differential operator

KW - Hadamard product

KW - Integral operator

KW - Salagean operator

UR - http://www.scopus.com/inward/record.url?scp=67650889312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650889312&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:67650889312

VL - 33

SP - 299

EP - 308

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

SN - 0972-0871

IS - 3

ER -