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Fekete–Szegő and Zalcman Functional Estimates for Subclasses of Alpha-Convex Functions Related to Trigonometric Functions

Author

Listed:
  • Krishnan Marimuthu

    (Department of Mathematics, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Chennai 600062, Tamilnadu, India
    These authors contributed equally to this work.)

  • Uma Jayaraman

    (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India
    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

In this study, we introduce the new subclasses, M α ( sin ) and M α ( cos ) , of α -convex functions associated with sine and cosine functions. First, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of the Zalcman functional for the class M α ( cos ) for the case n = 3 , proving that the Zalcman conjecture holds for this value of n . Moreover, the problem of the Fekete–Szegő functional estimate for these classes is studied.

Suggested Citation

  • Krishnan Marimuthu & Uma Jayaraman & Teodor Bulboacă, 2024. "Fekete–Szegő and Zalcman Functional Estimates for Subclasses of Alpha-Convex Functions Related to Trigonometric Functions," Mathematics, MDPI, vol. 12(2), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:234-:d:1316902
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