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Keywords = γ-Spirallikeness

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32 pages, 5835 KB  
Article
On Spirallikeness of Entire Functions
by Narjes Alabkary and Saiful R. Mondal
Mathematics 2025, 13(10), 1566; https://doi.org/10.3390/math13101566 - 9 May 2025
Cited by 1 | Viewed by 335
Abstract
In this article, we establish conditions under which certain entire functions represented as infinite products of their positive zeros are α-spirallike of order cos(α)/2. The discussion includes several examples featuring special functions such as Bessel, Struve, [...] Read more.
In this article, we establish conditions under which certain entire functions represented as infinite products of their positive zeros are α-spirallike of order cos(α)/2. The discussion includes several examples featuring special functions such as Bessel, Struve, Lommel, and q-Bessel functions. Full article
(This article belongs to the Special Issue Advances on Complex Analysis, 2nd Edition)
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15 pages, 309 KB  
Article
Radii of γ-Spirallike of q-Special Functions
by Sercan Kazımoğlu
Mathematics 2024, 12(14), 2261; https://doi.org/10.3390/math12142261 - 19 Jul 2024
Cited by 3 | Viewed by 1381
Abstract
The geometric properties of q-Bessel and q-Bessel-Struve functions are examined in this study. For each of them, three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. For [...] Read more.
The geometric properties of q-Bessel and q-Bessel-Struve functions are examined in this study. For each of them, three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. For these normalized functions, the radii of γ-spirallike and convex γ-spirallike of order σ are determined using their Hadamard factorization. These findings extend the known results for Bessel and Struve functions. The characterization of entire functions from the Laguerre-Pólya class plays an important role in our proofs. Additionally, the interlacing property of zeros of q-Bessel and q-Bessel-Struve functions and their derivatives is useful in the proof of our main theorems. Full article
11 pages, 1384 KB  
Article
Radius of Uniformly Convex γ-Spirallikeness of Combination of Derivatives of Bessel Functions
by Stanislawa Kanas and Kamaljeet Gangania
Axioms 2023, 12(5), 468; https://doi.org/10.3390/axioms12050468 - 12 May 2023
Cited by 5 | Viewed by 1540
Abstract
We find the sharp radius of uniformly convex γ-spirallikeness for Nν(z)=az2Jν(z)+bzJν(z)+cJν(z) (here [...] Read more.
We find the sharp radius of uniformly convex γ-spirallikeness for Nν(z)=az2Jν(z)+bzJν(z)+cJν(z) (here Jν(z) is the Bessel function of the first kind of order ν) with three different kinds of normalizations of the function Nν(z). As an application, we derive sufficient conditions on the parameters for the functions to be uniformly convex γ-spirallikeness and, consequently, generate examples of uniform convex γ-spirallike via Nν(z). Results are well-supported by the relevant graphs and tables. Full article
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13 pages, 316 KB  
Article
New Criteria for Convex-Exponent Product of Log-Harmonic Functions
by Rasoul Aghalary, Ali Ebadian, Nak Eun Cho and Mehri Alizadeh
Axioms 2023, 12(5), 409; https://doi.org/10.3390/axioms12050409 - 22 Apr 2023
Cited by 1 | Viewed by 1290
Abstract
In this study, we consider different types of convex-exponent products of elements of a certain class of log-harmonic mapping and then find sufficient conditions for them to be starlike log-harmonic functions. For instance, we show that, if f is a spirallike function, then [...] Read more.
In this study, we consider different types of convex-exponent products of elements of a certain class of log-harmonic mapping and then find sufficient conditions for them to be starlike log-harmonic functions. For instance, we show that, if f is a spirallike function, then choosing a suitable value of γ, the log-harmonic mapping F(z)=f(z)|f(z)|2γ is α-spiralike of order ρ. Our results generalize earlier work in the literature. Full article
(This article belongs to the Special Issue New Developments in Geometric Function Theory II)
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