Bi-Bazilevič functions based on the Mittag-Leffler-type Borel distribution associated with Legendre polynomials

Volume 24, Issue 3, pp 235--245 http://dx.doi.org/10.22436/jmcs.024.03.05

Publication Date: February 28, 2021 Submission Date: December 18, 2020 Revision Date: December 31, 2020 Accteptance Date: January 18, 2021

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Authors

Sheza. M. El-Deeb - Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah, Saudi Arabia. - Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt. G. Murugusundaramoorthy - Department of Mathematics, School of Advanced Sciences, Vellore Institute Technology University, Vellore-632014, India. Alhanouf Alburaikan - Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah, Saudi Arabia.

Abstract

In this paper, using the Mittag-Leffler-type Borel distribution, the authors introduce a new class of bi-Bazilevič functions defined in the open unit disc associated with Legendre polynomials, we find estimates for the general Taylor-Maclaurin coefficients of the functions in the subclass introduced, and the Fekete-Szego problem is solved.

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Keywords

• Bi-Bazilevič functions
• coefficient estimates
• Mittag-Leffler-type
• Borel distribution
• Legendre polynomials

MSC

•  30C45
•  30C50

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