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The Geometric Characterizations of the Ramanujan-Type Entire Function

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  • Khaled Mehrez

    (Department of Mathematics, Kairouan Preparatory Institute for Engineering Studies, University of Kairouan, Kairouan 3100, Tunisia
    Research Laboratory: Chemistry, Materials and Modeling (LR24ES02), Preparatory Institute for Engineering Studies of Kairouan, University of Kairouan, Kairouan 3100, Tunisia)

  • Abdulaziz Alenazi

    (Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia
    Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia)

Abstract

In the present paper, we present certain geometric properties, such as starlikeness, convexity of order η ( 0 ≤ η < 1 ) , and close-to-convexity, in an open unit disk of the normalized form of Ramanujan-type entire functions. As a consequence, a specific range of parameters is derived such that this function belongs to Hardy spaces H ∞ and H r . Finally, as an application, we present the monotonicity property of the Ramanujan-type entire function using the method of subordination factor sequences.

Suggested Citation

  • Khaled Mehrez & Abdulaziz Alenazi, 2025. "The Geometric Characterizations of the Ramanujan-Type Entire Function," Mathematics, MDPI, vol. 13(14), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2301-:d:1704528
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