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Inclusion Properties of p -Valent Functions Associated with Borel Distribution Functions

Author

Listed:
  • Ebrahim Amini

    (Department of Mathematics, Payme Noor University, Tehran P.O. Box 19395-4697, Iran)

  • Mojtaba Fardi

    (Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord P.O. Box 115, Iran)

  • Mahmoud A. Zaky

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13314, Saudi Arabia)

  • António M. Lopes

    (LAETA/INEGI, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal)

  • Ahmed S. Hendy

    (Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg 620002, Russia)

Abstract

In this paper, we define a differential operator on an open unit disk Δ by using the novel Borel distribution (BD) operator and means of convolution. This operator is adopted to introduce new subclasses of p -valent functions through the principle of differential subordination, and we focus on some interesting inclusion relations of these classes. Additionally, some inclusion relations are derived by using the Bernardi integral operator. Moreover, relevant convolution results are established for a class of analytic functions on Δ , and other results of analytic univalent functions are derived in detail. This study provides a new perspective for developing p -univalent functions with BD and offers valuable understanding for further research in complex analysis.

Suggested Citation

  • Ebrahim Amini & Mojtaba Fardi & Mahmoud A. Zaky & António M. Lopes & Ahmed S. Hendy, 2023. "Inclusion Properties of p -Valent Functions Associated with Borel Distribution Functions," Mathematics, MDPI, vol. 11(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3511-:d:1217068
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    References listed on IDEAS

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    1. A. K. Mishra & S. N. Kund, 2014. "Certain Families of Multivalent Analytic Functions Associated with Iterations of the Owa-Srivastava Fractional Differintegral Operator," Journal of Complex Analysis, Hindawi, vol. 2014, pages 1-9, October.
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