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Certain Properties of Harmonic Functions Defined by a Second-Order Differential Inequality

Author

Listed:
  • Daniel Breaz

    (Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania)

  • Abdullah Durmuş

    (Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University, 16059 Bursa, Turkey)

  • Sibel Yalçın

    (Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University, 16059 Bursa, Turkey)

  • Luminita-Ioana Cotirla

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

  • Hasan Bayram

    (Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University, 16059 Bursa, Turkey)

Abstract

The Theory of Complex Functions has been studied by many scientists and its application area has become a very wide subject. Harmonic functions play a crucial role in various fields of mathematics, physics, engineering, and other scientific disciplines. Of course, the main reason for maintaining this popularity is that it has an interdisciplinary field of application. This makes this subject important not only for those who work in pure mathematics, but also in fields with a deep-rooted history, such as engineering, physics, and software development. In this study, we will examine a subclass of Harmonic functions in the Theory of Geometric Functions. We will give some definitions necessary for this. Then, we will define a new subclass of complex-valued harmonic functions, and their coefficient relations, growth estimates, radius of univalency, radius of starlikeness and radius of convexity of this class are investigated. In addition, it is shown that this class is closed under convolution of its members.

Suggested Citation

  • Daniel Breaz & Abdullah Durmuş & Sibel Yalçın & Luminita-Ioana Cotirla & Hasan Bayram, 2023. "Certain Properties of Harmonic Functions Defined by a Second-Order Differential Inequality," Mathematics, MDPI, vol. 11(19), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4039-:d:1246190
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    References listed on IDEAS

    as
    1. Herb Silverman, 1994. "A class of bounded starlike functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-4, January.
    2. Georgia Irina Oros & Sibel Yalçın & Hasan Bayram, 2023. "Some Properties of Certain Multivalent Harmonic Functions," Mathematics, MDPI, vol. 11(11), pages 1-12, May.
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    Cited by:

    1. Sibel Yalçın & Hasan Bayram & Georgia Irina Oros, 2024. "Some Properties and Graphical Applications of a New Subclass of Harmonic Functions Defined by a Differential Inequality," Mathematics, MDPI, vol. 12(15), pages 1-15, July.

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    1. Sibel Yalçın & Hasan Bayram & Georgia Irina Oros, 2024. "Some Properties and Graphical Applications of a New Subclass of Harmonic Functions Defined by a Differential Inequality," Mathematics, MDPI, vol. 12(15), pages 1-15, July.

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