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Bulletin of the Iranian Mathematical Society

, Volume 44, Issue 1, pp 149–157 | Cite as

Faber Polynomial Coefficient Estimates for Bi-univalent Functions Defined by the Tremblay Fractional Derivative Operator

  • H. M. Srivastava
  • S. Sümer EkerEmail author
  • S. G. Hamidi
  • J. M. Jahangiri
Original Paper

Abstract

Using the Tremblay fractional derivative operator in the complex domain, we introduce and investigate a new class of analytic and bi-univalent functions in the open unit disk. We use the Faber polynomial expansions to obtain upper bounds for the general coefficients of such functions subject to a gap series condition as well as obtaining bounds for their first two coefficients.

Keywords

Tremblay fractional derivative operator Faber polynomials Analytic Univalent Bi-univalent functions 

Mathematics Subject Classification

Primary 30C45 Secondary 30C50 30C80 

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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  • H. M. Srivastava
    • 1
    • 2
  • S. Sümer Eker
    • 3
    Email author
  • S. G. Hamidi
    • 4
  • J. M. Jahangiri
    • 5
  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  2. 2.Department of Medical Research, China Medical University HospitalChina Medical UniversityTaichungTaiwan, Republic of China
  3. 3.Department of Mathematics, Faculty of ScienceDicle UniversityDiyarbakirTurkey
  4. 4.Department of MathematicsBrigham Young UniversityProvoUSA
  5. 5.Department of Mathematical SciencesKent State UniversityBurtonUSA

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