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Coefficient bounds for a subclass of univalent functions of complex order associated with Chebyshev polynomials defined by \(q-\) derivative operator

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Abstract

In this paper, we investigate a subclass \(L(q,b,\alpha ,t)\) by means of Chebyshev polynomials and \(q-\) derivative operator expansions of univalent functions of complex order in the open unit disk. Later, we find initial coefficients \(|a_{2}|\)and \(|a_{3}|\) and sharp bounds of Fekete–Szegő functional \(|a_{3}-\xi a_{2}^{2}|\) for functions in this subclass.

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Acknowledgements

The authors are extremely grateful to the editor and the anonymous reviewers for their valuable comments and helpful suggestions which helped to improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    M. K. Aouf & A. O. Mostafa

  2. Department of Mathematics, Faculty of Education, Amran University, Amran, Yemen

    F. Y. Al-Quhali

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  1. M. K. Aouf
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  2. A. O. Mostafa
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  3. F. Y. Al-Quhali
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Correspondence to F. Y. Al-Quhali.

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Aouf, M.K., Mostafa, A.O. & Al-Quhali, F.Y. Coefficient bounds for a subclass of univalent functions of complex order associated with Chebyshev polynomials defined by \(q-\) derivative operator. Afr. Mat. 34, 61 (2023). https://doi.org/10.1007/s13370-023-01088-y

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