On the fekete-szegö theorem for the generalized owa-srivastava operator

Aisha Ajwely, Maslina Darus

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let A be the class of analytic functions in the open unit disk U = {z : z <1}. The sharp bound is obtained for the coefficient functional |a 3 - μa2 2|, where μεC or and are respectively the second and the third coefficient for f belonging to a certain subclass Rα,β(γ,ρ) defined by a fractional operator. By specializing the parameters α,β,γ and ρ, many consequence results are obtained. Further, an improvement for the estimation of |a3 - μa2 2| is investigated by dividing the intervals of μ ε R. In addition, sharp estimates for the first few coefficients of the inverse functions of R α,β(γ,ρ) are derived.

Original languageEnglish
Pages (from-to)179-188
Number of pages10
JournalProceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science
Volume12
Issue number3
Publication statusPublished - Jul 2011

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Mathematical operators
theorems
operators
Coefficient
coefficients
Operator
Theorem
analytic functions
Inverse function
Sharp Bound
Unit Disk
Analytic function
Fractional
intervals
Interval
estimates
Estimate
Class

Keywords

  • Coefficient inequality
  • Fekete-Szegö inequality
  • Fractional derivative
  • Hankel determinant

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)
  • Computer Science(all)

Cite this

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AB - Let A be the class of analytic functions in the open unit disk U = {z : z <1}. The sharp bound is obtained for the coefficient functional |a 3 - μa2 2|, where μεC or and are respectively the second and the third coefficient for f belonging to a certain subclass Rα,β(γ,ρ) defined by a fractional operator. By specializing the parameters α,β,γ and ρ, many consequence results are obtained. Further, an improvement for the estimation of |a3 - μa2 2| is investigated by dividing the intervals of μ ε R. In addition, sharp estimates for the first few coefficients of the inverse functions of R α,β(γ,ρ) are derived.

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