The Faber polynomial expansion method and the Taylor-Maclaurin coefficient estimates of Bi-Close-to-Convex functions connected with the <em>q</em>-convolution

H. M. Srivastava; Sheza M. El-Deeb; H. M. Srivastava; Sheza M. El-Deeb

doi:10.3934/math.2020454

AIMS Mathematics

2020, Volume 5, Issue 6: 7087-7106. doi: 10.3934/math.2020454

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The Faber polynomial expansion method and the Taylor-Maclaurin coefficient estimates of Bi-Close-to-Convex functions connected with the q-convolution

H. M. Srivastava ^{1,2,3
,
,},
Sheza M. El-Deeb ^4,5

1.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China
3.
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
4.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
5.
Department of Mathematics, College of Science and Arts in Badaya, Qassim University, P.O. Box: 6640, Buraidah 51452, Saudi Arabia

Received: 01 August 2020 Accepted: 03 September 2020 Published: 10 September 2020
MSC : Primary: 05A30, 30C45; Secondary: 11B65, 47B38

In this paper, we introduce a new class of analytic and bi-close-to-convex functions connected with q-convolution, which are defined in the open unit disk. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this subclass by using the Faber polynomial expansion method. Several corollaries and consequences of our main results are also briefly indicated.
Citation: H. M. Srivastava, Sheza M. El-Deeb. The Faber polynomial expansion method and the Taylor-Maclaurin coefficient estimates of Bi-Close-to-Convex functions connected with the q-convolution[J]. AIMS Mathematics, 2020, 5(6): 7087-7106. doi: 10.3934/math.2020454

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Abstract

In this paper, we introduce a new class of analytic and bi-close-to-convex functions connected with q-convolution, which are defined in the open unit disk. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this subclass by using the Faber polynomial expansion method. Several corollaries and consequences of our main results are also briefly indicated.

References

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