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Sharp Coefficient Bounds for a New Subclass of Starlike Functions of Complex Order γ Associated with Cardioid Domain

Author

Listed:
  • Suha B. Al-Shaikh

    (Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia)

  • Khaled Matarneh

    (Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia)

  • Ahmad A. Abubaker

    (Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia)

  • Mohammad Faisal Khan

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

Abstract

In this study, by using the concepts of subordination, we define a new family R M , N , λ , γ of starlike functions of complex order γ connected with the cardioid domain. The main contribution of this article consists of the derivations of sharp inequality, considering the functions belonging to the family R M , N , λ , γ of starlike functions in U . Particularly, sharp bounds of the first two Taylor–Maclaurin coefficients, sharp estimates of the Fekete–Szegö-type functionals, and coefficient inequalities are investigated for this newly defined family R M , N , λ , γ of starlike functions. Furthermore, for the inverse function and the log g ( z ) z function, we investigate the same types of problems. Several well-known corollaries are also highlighted to show the connections between prior research and the new findings.

Suggested Citation

  • Suha B. Al-Shaikh & Khaled Matarneh & Ahmad A. Abubaker & Mohammad Faisal Khan, 2023. "Sharp Coefficient Bounds for a New Subclass of Starlike Functions of Complex Order γ Associated with Cardioid Domain," Mathematics, MDPI, vol. 11(9), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2017-:d:1131401
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    References listed on IDEAS

    as
    1. Sarfraz Nawaz Malik & Shahid Mahmood & Mohsan Raza & Sumbal Farman & Saira Zainab, 2018. "Coefficient Inequalities of Functions Associated with Petal Type Domains," Mathematics, MDPI, vol. 6(12), pages 1-11, December.
    2. Sondekola Rudra Swamy & Basem Aref Frasin & Ibtisam Aldawish, 2022. "Fekete–Szegö Functional Problem for a Special Family of m -Fold Symmetric Bi-Univalent Functions," Mathematics, MDPI, vol. 10(7), pages 1-14, April.
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