Some subclasses of analytic functions of complex order defined by new differential operator

Maslina Darus, Imran Faisal

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let A(n) denote the class of analytic functions f in the open unit disk U = {z : |z| < 1} normalized by f (0) = f′(0)-1 = 0. In this paper, we introduce and study the classes S n,μ(γ,α,β, λ,Ω) and R n,μ(γ,α,β,λ, Ω) of functions f ∈l A(n) with (μ)z(D λ Ω+2(α,ω) f (z))′ +(1-μ)z(D λ Ω+1 λ (α,ω) f (z))′ ≠ 0 and satisfy some conditions available in literature, where f ∈ A(n),α,ω,μ ≥ 0,Ω ∈ N∪{0}, z ∈U, and D λ m(α,ω) f (z) :A → A, is the linear fractional differential operator, newly defined as follows D λ m(α,ω) f (z)= z + ∑ k=2 a k(1+(k -1) λω α) mz k·Several properties such as coefficient estimates, growth and distortion theorems, extreme points, integral means inequalities and inclusion for the functions included in the classes S n,μ(γ,α,β,λ, Ω,ω) and R n,μ(γ,α,β, λ,Ω,ω) are given.

Original languageEnglish
Pages (from-to)223-242
Number of pages20
JournalTamkang Journal of Mathematics
Volume43
Issue number2
DOIs
Publication statusPublished - Jun 2012

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Mathematical operators
Differential operator
Analytic function
Distortion Theorem
Integral Means
Coefficient Estimates
Extreme Points
Unit Disk
Fractional
Inclusion
Denote
Class

Keywords

  • (n,σ)-neighborhoods
  • Analytic functions
  • Coefficient estimates
  • Convex function
  • Differential operator
  • Extreme points
  • Growth and distortion theorems
  • Hadamard product
  • Identity function
  • Inclusion properties
  • Neighborhoods properties

ASJC Scopus subject areas

  • Metals and Alloys
  • Materials Science(all)

Cite this

Some subclasses of analytic functions of complex order defined by new differential operator. / Darus, Maslina; Faisal, Imran.

In: Tamkang Journal of Mathematics, Vol. 43, No. 2, 06.2012, p. 223-242.

Research output: Contribution to journalArticle

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