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Subordination Properties of Meromorphic Kummer Function Correlated with Hurwitz–Lerch Zeta-Function

Author

Listed:
  • Firas Ghanim

    (Department of Mathematics, College of Sciences, University of Sharjah, Sharjah 27272, UAE)

  • Khalifa Al-Shaqsi

    (Department of Information Technology, University of Technology and Applied Science, Nizwa College of Technology, P.O. Box 75, Nizwa 612, Oman)

  • Maslina Darus

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor D. Ehsan, Malaysia)

  • Hiba Fawzi Al-Janaby

    (Department of Mathematics, College of Science, University of Baghdad, Baghdad 10081, Iraq)

Abstract

Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Function Theory (SPFT), are significant in developing and providing further new studies. In complex domain, the convolution tool is a salutary technique for systematic analytical characterization of geometric functions. The analytic functions in the punctured unit disk are the so-called meromorphic functions. In this present analysis, a new convolution complex operator defined on meromorphic functions related with the Hurwitz-Lerch Zeta type functions and Kummer functions is considered. Certain sufficient stipulations are stated for several formulas of this defining operator to attain subordination. Indeed, these outcomes are an extension of known outcomes of starlikeness, convexity, and close to convexity.

Suggested Citation

  • Firas Ghanim & Khalifa Al-Shaqsi & Maslina Darus & Hiba Fawzi Al-Janaby, 2021. "Subordination Properties of Meromorphic Kummer Function Correlated with Hurwitz–Lerch Zeta-Function," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:192-:d:482913
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    References listed on IDEAS

    as
    1. F. Ghanim, 2013. "A Study of a Certain Subclass of Hurwitz-Lerch-Zeta Function Related to a Linear Operator," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, September.
    2. Srivastava, H.M. & Gaboury, S. & Ghanim, F., 2015. "Some further properties of a linear operator associated with the λ-generalized Hurwitz–Lerch zeta function related to the class of meromorphically univalent functions," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 1019-1029.
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    Cited by:

    1. F. Ghanim & Hiba F. Al-Janaby & Marwan Al-Momani & Belal Batiha, 2022. "Geometric Studies on Mittag-Leffler Type Function Involving a New Integrodifferential Operator," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    2. Georgia Irina Oros, 2022. "Geometrical Theory of Analytic Functions," Mathematics, MDPI, vol. 10(18), pages 1-4, September.

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