The Geometric Characterizations of the Ramanujan-Type Entire Function

Khaled Mehrez and Abdulaziz Alenazi ()
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Khaled Mehrez: Department of Mathematics, Kairouan Preparatory Institute for Engineering Studies, University of Kairouan, Kairouan 3100, Tunisia
Abdulaziz Alenazi: Department of Mathematics, College of Science, Northern Border University, Arar 73213, Saudi Arabia

Mathematics, 2025, vol. 13, issue 14, 1-18

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.

Keywords: Ramanujan-type entire functions; univalent functions; analytic functions; close-to-convex functions; starlike functions; convex functions; subordination factor sequence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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