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19 pages, 464 KB

Open AccessArticle

Estimating 2,3-Fold Hankel Determinants, Zalcman Functionals and Logarithmic Coefficients of Certain Subclasses of Holomorphic Functions with Bounded Rotations

by Farouq Alshormani, Bushra Kanwal, Faiza Attiq, Amr M. Y. Abdelaty, Alina Alb Lupas and Ibrahim S. Elshazly

Symmetry 2026, 18(1), 51; https://doi.org/10.3390/sym18010051 (registering DOI) - 26 Dec 2025

Abstract

The study explores analytic, geometric and algebaraic properties of two subclasses of analytic functions: the class of Bounded Radius Rotation denoted by

R_{s},_{ϱ} (A, B, z)

, and the class of Bounded Boundary Rotation denoted by [...] Read more.

The study explores analytic, geometric and algebaraic properties of two subclasses of analytic functions: the class of Bounded Radius Rotation denoted by

R_{s},_{ϱ} (A, B, z)

, and the class of Bounded Boundary Rotation denoted by

V_{s},_{ϱ} (A, B, z)

, both associated with strongly Janowski type functions. In particular, we obtain upper bounds for the third-order Hankel determinant

| H_{3, 1} f (z) |

and concentrate on functions displaying 2- and 3-fold symmetry. We also provide estimates for the initial logarithmic coefficients

η_{1}, η_{2}, η_{3}

and the Zalcman functional

| t_{3}^{2} - t_{5} |

for each class. These findings provide fresh insights into the behavior of generalized subclasses of univalent function. Full article

(This article belongs to the Section Mathematics)

17 pages, 313 KB

Open AccessArticle

Faber Polynomial Coefficient Estimates of m-Fold Symmetric Bi-Univalent Functions with Bounded Boundary Rotation

by Anandan Murugan, Srikandan Sivasubramanian, Prathviraj Sharma and Gangadharan Murugusundaramoorthy

Mathematics 2024, 12(24), 3963; https://doi.org/10.3390/math12243963 - 17 Dec 2024

Viewed by 893

Abstract

In the current article, we introduce several new subclasses of m-fold symmetric analytic and bi-univalent functions associated with bounded boundary and bounded radius rotation within the open unit disk

D .

Utilizing the Faber polynomial expansion, we derive upper bounds for the [...] Read more.

D .

Utilizing the Faber polynomial expansion, we derive upper bounds for the coefficients

| b_{m k + 1} |

and establish initial coefficient bounds for

| b_{m + 1} |

and

| b_{2 m + 1} | .

Additionally, we explore the Fekete–Szegö inequalities applicable to the functions that fall within these newly defined subclasses. Full article

(This article belongs to the Section B: Geometry and Topology)

14 pages, 280 KB

Open AccessArticle

Coefficient Estimates for New Subclasses of Bi-Univalent Functions with Bounded Boundary Rotation by Using Faber Polynomial Technique

by Huo Tang, Prathviraj Sharma and Srikandan Sivasubramanian

Axioms 2024, 13(8), 509; https://doi.org/10.3390/axioms13080509 - 28 Jul 2024

Cited by 2 | Viewed by 1133

Abstract

In this article, the authors use the Faber polynomial expansions to find the general coefficient estimates for a few new subclasses of bi-univalent functions with bounded boundary rotation and bounded radius rotation. Some of the results improve the existing coefficient bounds in the [...] Read more.

(This article belongs to the Special Issue Advances in Geometric Function Theory and Related Topics)

16 pages, 558 KB

Open AccessArticle

On Ozaki Close-to-Convex Functions with Bounded Boundary Rotation

by Prathviraj Sharma, Asma Alharbi, Srikandan Sivasubramanian and Sheza M. El-Deeb

Symmetry 2024, 16(7), 839; https://doi.org/10.3390/sym16070839 - 3 Jul 2024

Cited by 3 | Viewed by 1813

Abstract

In the present investigation, we introduce a new subclass of univalent functions

F (u, λ)

and a subclass of bi-univalent function

F_{o, Σ} (u, λ)

with bounded boundary and bounded radius rotation. Some examples of [...] Read more.

In the present investigation, we introduce a new subclass of univalent functions

F (u, λ)

and a subclass of bi-univalent function

F_{o, Σ} (u, λ)

with bounded boundary and bounded radius rotation. Some examples of the functions belonging to the classes

F (u, λ)

are also derived. For these new classes, the authors derive many interesting relations between these classes and the existing familiar subclasses in the literature. Furthermore, the authors establish new coefficient estimates for these classes. Apart from the above, the first two initial coefficient bounds for the class

F_{o, Σ} (u, λ)

are established. Full article

(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)

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14 pages, 273 KB

Open AccessArticle

Some Subclasses of Uniformly Univalent Functions with Respect to Symmetric Points

by Shahid Mahmood, Hari M. Srivastava and Sarfraz Nawaz Malik

Symmetry 2019, 11(2), 287; https://doi.org/10.3390/sym11020287 - 22 Feb 2019

Cited by 9 | Viewed by 2991

Abstract

This article presents the study of certain analytic functions defined by bounded radius rotations associated with conic domain. Many geometric properties like coefficient estimate, radii problems, arc length, integral representation, inclusion results and growth rate of coefficients of Taylor’s series representation are investigated. [...] Read more.

(This article belongs to the Special Issue Integral Transforms and Operational Calculus)

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