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Coefficient estimates for a general subclass of analytic and bi-univalent functions of the Ma–Minda type

  • H. M. Srivastava
  • S. Gaboury
  • F. Ghanim
Original Paper
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Abstract

In the present investigation, we consider a new general subclass \(\mathcal {S}_{\Sigma }(\tau , \mu , \lambda , \gamma ; \phi )\) of the class \(\Sigma \) consisting of normalized analytic and bi-univalent functions in the open unit disk \(\mathbb {U}\). For functions belonging to the class introduced here, we find estimates on the Taylor-Maclaurin coeffcients \(|a_{2}|\) and \(|a_{3}|\). Several connections to some of the earlier known results are also pointed out.

Keywords

Analytic functions Bi-Univalent functions Coefficient estimates Bi-Starlike and bi-convex functions of complex order Principle of subordination 

Mathematics Subject Classifications

Primary 30C45 Secondary 30C50 30C80 
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© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  2. 2.Department of Medical Research, China Medical University HospitalChina Medical UniversityTaiwanRepublic of China
  3. 3.Department of Mathematics and Computer ScienceUniversity of Québec at ChicoutimiChicoutimiCanada
  4. 4.Department of Mathematics, College of SciencesUniversity of SharjahSharjahUnited Arab Emirates

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