Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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BI-UNIVALENT FUNCTIONS CONNECTED WITH THE MITTAG-LEFFLER-TYPE BOREL DISTRIBUTION BASED UPON THE LEGENDRE POLYNOMIALS

  • El-Deeb, Sheza M. (Department of Mathematics, College of Science and Arts Al-Badaya Qassim University, Department of Mathematics, Faculty of Science, Damietta University) ;
  • Murugusundaramoorthy, Gangadharan (Department of Mathematics, School of Advanced Sciences Vellore Institute Technology University) ;
  • Alburaikan, Alhanouf (Department of Mathematics, College of Science and Arts Al-Badaya Qassim University)
  • Received : 2021.11.11
  • Accepted : 2021.12.02
  • Published : 2022.06.08
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Abstract

In this paper, we introduce new subclasses of analytic and bi-univalent functions associated with the Mittag-Leffler-type Borel distribution by using the Legendre polynomials. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3| for functions in these subclasses and obtain Fekete-Szegő problem for these subclasses. We also state certain new subclasses of Σ and initial coefficient estimates and Fekete-Szegő inequalities.

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Acknowledgement

The authors are grateful to the reviewers for their valuable remarks and advices that help us to improve the quality of the paper in present form.

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