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New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q -Calculus

Author

Listed:
  • Ridong Wang

    (School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China)

  • Manoj Singh

    (Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia)

  • Shahid Khan

    (Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan)

  • Huo Tang

    (School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, China)

  • Mohammad Faisal Khan

    (Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia)

  • Mustafa Kamal

    (Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia)

Abstract

In this investigation, the q -difference operator and the Sălăgean q -differential operator are utilized to establish novel subclasses of analytical bi-close-to-convex functions. We determine the general Taylor–Maclaurin coefficient of the functions in this class using the Faber polynomial method. We demonstrate the unpredictable behaviour of initial coefficients a 2 , a 3 and investigate the Fekete–Szegő problem a 3 − a 2 2 for the subclasses of bi-close-to-convex functions. To highlight the connections between existing knowledge and new research, certain known and unknown corollaries are also highlighted.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1217-:d:1085180
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    References listed on IDEAS

    as
    1. Jie Zhai & Rekha Srivastava & Jin-Lin Liu, 2022. "Faber Polynomial Coefficient Estimates of Bi-Close-to-Convex Functions Associated with Generalized Hypergeometric Functions," Mathematics, MDPI, vol. 10(17), pages 1-11, August.
    2. Ibrar Ahmad & Syed Ghoos Ali Shah & Saqib Hussain & Maslina Darus & Babar Ahmad & Firdous A. Shah, 2022. "Fekete-Szegö Functional for Bi-univalent Functions Related with Gegenbauer Polynomials," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, April.
    3. 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.
    4. Saqib Hussain & Shahid Khan & Muhammad Asad Zaighum & Maslina Darus & Zahid Shareef, 2017. "Coefficients Bounds for Certain Subclass of Biunivalent Functions Associated with Ruscheweyh -Differential Operator," Journal of Complex Analysis, Hindawi, vol. 2017, pages 1-9, September.
    5. Samaneh G. Hamidi & Suzeini Abd Halim & Jay M. Jahangiri, 2013. "Faber Polynomial Coefficient Estimates for Meromorphic Bi-Starlike Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-4, March.
    6. 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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