Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 16 (2021), 193 -- 205

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This work is licensed under a Creative Commons Attribution 4.0 International License.

A CERTAIN FAMILY OF BI-UNIVALENT FUNCTIONS ASSOCIATED WITH THE PASCAL DISTRIBUTION SERIES BASED UPON THE HORADAM POLYNOMIALS

H. M. Srivastava, A. K. Wanas and G. Murugusundaramoorthy

Abstract. The purpose of this article is to introduce a new subclass ℋΣ(δ,λ,m,θ,x) of analytic and bi-univalent functions by using the Horadam polynomials, which is associated with the Pascal distribution series and to investigate the bounds for |a2| and |a3|, where a2, a3 are the initial Taylor-Maclaurin coefficients. Further we obtain the Fekete-Szegö inequality for functions in the class ℋΣ(δ,λ,m,θ,x) which we have introduced here.

2020 Mathematics Subject Classification: Primary 30C45; Secondary 11B39, 30C50, 33C05.
Keywords: analytic functions; univalent functions; bi-univalent functions; Horadam polynomials; Upper bounds; Fekete-Szegö problem; Pascal distribution series; Subordination between analytic functions.

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H. M. Srivastava
Department of Mathematics and Statistics, University of Victoria,
Victoria, British Columbia V8W 3R4, Canada.
and
Department of Medical Research, China Medical University Hospital,
China Medical University, Taichung 40402, Taiwan, Republic of China.
and
Department of Mathematics and Informatics, Azerbaijan University,
71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
e-mail: harimsri@math.uvic.ca


A. K. Wanas
Department of Mathematics, College of Science, University of Al-Qadisiyah,
Al Diwaniyah, Al-Qadisiyah, Iraq.
e-mail: abbas.kareem.w@qu.edu.iq


G. Murugusundaramoorthy (corresponding author)
Department of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology (Deemed to be University),
Vellore 632014, Tamil Nadu, India.
e-mail: gmsmoorthy@yahoo.com

http://www.utgjiu.ro/math/sma