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New Applications of Gegenbauer Polynomials on a New Family of Bi-Bazilevič Functions Governed by the q -Srivastava-Attiya Operator

Author

Listed:
  • Abbas Kareem Wanas

    (Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah 58801, Iraq)

  • Luminiţa-Ioana Cotîrlǎ

    (Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania)

Abstract

In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family J Σ ( λ , γ , s , t , q ; h ) of holomorphic and bi-univalent functions which were defined in the unit disk D associated with the q -Srivastava–Attiya operator. We establish the bounds for | a 2 | and | a 3 | , where a 2 , a 3 are the initial Taylor–Maclaurin coefficients. For the new family of functions J Σ ( λ , γ , s , t , q ; h ) we investigate the Fekete-Szegö inequality, special cases and consequences.

Suggested Citation

  • Abbas Kareem Wanas & Luminiţa-Ioana Cotîrlǎ, 2022. "New Applications of Gegenbauer Polynomials on a New Family of Bi-Bazilevič Functions Governed by the q -Srivastava-Attiya Operator," Mathematics, MDPI, vol. 10(8), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1309-:d:794012
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    References listed on IDEAS

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    1. Georgia Irina Oros & Luminiţa-Ioana Cotîrlă, 2022. "Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m -Fold Symmetric Bi-Univalent Functions," Mathematics, MDPI, vol. 10(1), pages 1-12, January.
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    Cited by:

    1. Ridong Wang & Manoj Singh & Shahid Khan & Huo Tang & Mohammad Faisal Khan & Mustafa Kamal, 2023. "New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q -Calculus," Mathematics, MDPI, vol. 11(5), pages 1-15, March.

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