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On Bi-Univalent Function Classes Defined via Gregory Polynomials

by Ibtisam Aldawish, Mallikarjun G. Shrigan, Sheza El-Deeb and Hari M. Srivastava

Mathematics 2025, 13(19), 3121; https://doi.org/10.3390/math13193121 - 29 Sep 2025

Viewed by 571

In this paper, we introduce and study a new subclass of bi-univalent functions related to Mittag–Leffler functions associated with Gregory polynomials and satisfy certain subordination conditions defined in the open unit disk. We derive coefficient bounds for the Taylor–Maclaurin coefficients [...] Read more.

| γ_{2} |

and

| γ_{3} |

, and also explore the Fekete–Szegö functional. Full article

(This article belongs to the Section C4: Complex Analysis)

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22 pages, 810 KB

Open AccessArticle

Gregory Polynomials Within Sakaguchi-Type Function Classes: Analytical Estimates and Geometric Behavior

by Arzu Akgül and Georgia Irina Oros

Symmetry 2025, 17(6), 884; https://doi.org/10.3390/sym17060884 - 5 Jun 2025

Cited by 1 | Viewed by 873

Abstract

This work introduces a novel family of analytic and univalent functions formulated through the integration of Gregory coefficients and Sakaguchi-type functions. Employing subordination techniques, we obtain sharp bounds for the initial coefficients in their Taylor expansions. The influence of parameter variations is examined through comprehensive geometric visualizations, which confirm the non-emptiness of the class and provide insights into its structural properties. Furthermore, Fekete–Szegö inequalities are established, enriching the theory of bi-univalent functions. The combination of analytical methods and geometric representations offers a versatile framework for future research in geometric function theory. Full article

(This article belongs to the Special Issue Applications of Special Functions in Complex Analysis and Their Symmetries)

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12 pages, 280 KB

Open AccessArticle

Generalized Bounded Turning Functions Connected with Gregory Coefficients

by Huo Tang, Zeeshan Mujahid, Nazar Khan, Fairouz Tchier and Muhammad Ghaffar Khan

Axioms 2024, 13(6), 359; https://doi.org/10.3390/axioms13060359 - 28 May 2024

Cited by 4 | Viewed by 1727

Abstract

In this research article, we introduce new family

R_{G}

In this research article, we introduce new family

R_{G}

of holomorphic functions, which is related to the generalized bounded turning and generating functions of Gregory coefficients. Leveraging the concept of functions with positive real parts, we acquire the first five coefficients for the functions belonging to this newly defined family, demonstrating their sharpness. Furthermore, we find the third Hankel determinant for functions in the class

R_{G}

. Moreover, the sharp bounds for logarithmic and inverse coefficients of functions belonging to the under-considered class

R_{G}

are estimated. Full article

(This article belongs to the Special Issue New Developments in Geometric Function Theory, 3rd Edition)

16 pages, 472 KB

Open AccessArticle

Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients

by Gangadharan Murugusundaramoorthy, Kaliappan Vijaya and Teodor Bulboacă

Mathematics 2023, 11(13), 2857; https://doi.org/10.3390/math11132857 - 26 Jun 2023

Cited by 17 | Viewed by 2179

Abstract

In this article we introduce three new subclasses of the class of bi-univalent functions

Σ

, namely

{HG}_{Σ}

{GM}_{Σ} (μ)

and

G_{Σ} (λ)

, by using the subordinations with the functions whose coefficients are Gregory [...] Read more.

In this article we introduce three new subclasses of the class of bi-univalent functions

Σ

, namely

{HG}_{Σ}

{GM}_{Σ} (μ)

and

G_{Σ} (λ)

, by using the subordinations with the functions whose coefficients are Gregory numbers. First, we evidence that these classes are not empty, i.e., they contain other functions besides the identity one. For functions in each of these three bi-univalent function classes, we investigate the estimates

|a_{2}|

and

|a_{3}|

of the Taylor–Maclaurin coefficients and Fekete–Szegő functional problems. The main results are followed by some particular cases, and the novelty of the characterizations and the proofs may lead to further studies of such types of similarly defined subclasses of analytic bi-univalent functions. Full article

(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)

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17 pages, 3441 KB

Open AccessArticle

Consensus Genetic Linkage Map Construction Based on One Common Parental Line for QTL Mapping in Wheat

by Xin Hu, Yingquan Zhang, Jingjuan Zhang, Shahidul Islam, Maoyun She, Yun Zhao, Guixiang Tang, Yanjie Jiang, Junkang Rong and Wujun Ma

Agronomy 2021, 11(2), 227; https://doi.org/10.3390/agronomy11020227 - 26 Jan 2021

Cited by 3 | Viewed by 4394

Abstract

The consensus map is used for the verification of marker order, quantitative trait locus (QTL) mapping and molecular marker-assisted selection (MAS) in wheat breeding. In this study, a wheat consensus genetic map named as Sp7A_G7A, was constructed using 5643 SNP markers in two double haploid (DH) populations of Spitfire × Bethlehem-7AS (Sp7A) and Gregory × Bethlehem-7AS (G7A), covering 4376.70 cM of 21 chromosomes (chr) with an average interval of 0.78 cM. The collinearity of the linkage maps with the consensus map of Con_map_Wang2014 and the physical map of wheat reference genome (IWGSC RefSeq v1.0) were analyzed based on the Spearman rank correlation coefficients. As results, the three constructed genetic maps of Sp7A, G7A and Sp7A_G7A showed high collinearity with the Con_map_Wang2014 and the physical map, and importantly, the collinearity level between our constructed maps and the wheat physical map is higher than that between the Con_map_Wang2014 and the physical map. The seed coat color QTL detected in both populations under multiple environments were on the region (745.73–760.14 Mbp) of the seed color gene R-B1/Tamyb10-B1 (TraesCS3B02G515900, 3B: 757,918,264–757,920,082 bp). The validated consensus map will be beneficial for QTL mapping, positional cloning, meta-QTL analysis and wheat breading. Full article

(This article belongs to the Special Issue Novel Breeding Technologies in Cereal Crops)

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