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Logarithmic Coefficients Inequality for the Family of Functions Convex in One Direction

Author

Listed:
  • Ebrahim Analouei Adegani

    (Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood P.O. Box 316-36155, Iran
    These authors contributed equally to this work.)

  • Ahmad Motamednezhad

    (Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood P.O. Box 316-36155, Iran
    These authors contributed equally to this work.)

  • Mostafa Jafari

    (Department of Mathematics, Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 66414, Iran
    These authors contributed equally to this work.)

  • Teodor Bulboacă

    (Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

Abstract

The logarithmic coefficients play an important role for different estimates in the theory of univalent functions. Due to the significance of the recent studies about the logarithmic coefficients, the problem of obtaining the sharp bounds for the modulus of these coefficients has received attention. In this research, we obtain sharp bounds of the inequality involving the logarithmic coefficients for the functions of the well-known class G and investigate a majorization problem for the functions belonging to this family. To prove our main results, we use the Briot–Bouquet differential subordination obtained by J.A. Antonino and S.S. Miller and the result of T.J. Suffridge connected to the Alexander integral. Combining these results, we give sharp inequalities for two types of sums involving the modules of the logarithmical coefficients of the functions of the class G indicating also the extremal function. In addition, we prove an inequality for the modulus of the derivative of two majorized functions of the class G , followed by an application.

Suggested Citation

  • Ebrahim Analouei Adegani & Ahmad Motamednezhad & Mostafa Jafari & Teodor Bulboacă, 2023. "Logarithmic Coefficients Inequality for the Family of Functions Convex in One Direction," Mathematics, MDPI, vol. 11(9), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2140-:d:1138487
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    References listed on IDEAS

    as
    1. Maksim V. Kukushkin, 2022. "Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent," Mathematics, MDPI, vol. 10(13), pages 1-27, June.
    2. Davood Alimohammadi & Nak Eun Cho & Ebrahim Analouei Adegani & Ahmad Motamednezhad, 2020. "Argument and Coefficient Estimates for Certain Analytic Functions," Mathematics, MDPI, vol. 8(1), pages 1-14, January.
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