Fekete–Szegö functional problems for some subclasses of bi-univalent functions defined by Frasin differential operator

  • Feras YousefEmail author
  • Tariq Al-Hawary
  • G. Murugusundaramoorthy


In this paper, we introduce a new subclass \(\mathcal {B}_{\Sigma }^{\zeta }(m,\gamma ,\lambda ;\varphi )\) of bi-univalent functions defined by a new differential operator of analytic functions involving binomial series due to Frasin (Bol Soc Paran Mat (in press), 2019) in the open unit disk. We obtain coefficient bounds for the Taylor–Maclaurin coefficients \(|a_{2}|\) and \(|a_{3}|\) of the function \(f\in \mathcal {B}_{\Sigma }^{\zeta }(m,\gamma ,\lambda ;\varphi )\). Furthermore, we solve the Fekete–Szegö functional problem for functions in \(\mathcal {B}_{\Sigma }^{\zeta }(m,\gamma ,\lambda ;\varphi )\). The results presented in this paper improve or generalize the earlier results of Peng and Han (Acta Math Sci 34(1):228–240, 2014) and Tang et al. (J Math Inequal 10(4):1063–1092, 2016).


Analytic functions Univalent functions Bi-univalent functions Taylor–Maclaurin series Binomial series Coefficient inequalities Fekete–Szegö problems 

Mathematics Subject Classification




The authors would like to thank the referees for their useful comments and suggestions to improve the original manuscript.


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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceThe University of JordanAmmanJordan
  2. 2.Department of Applied Science, Ajloun CollegeAl-Balqa Applied UniversityAjlounJordan
  3. 3.School of Advanced SciencesVellore Institute of Technology (VIT)VelloreIndia

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