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12 pages, 29719 KB

Open AccessArticle

Coefficient Bounds for New Subclass of Starlike Functions with Respect to Symmetric Points Associated with an Epicycloid

by Büşra Körfeci and Hatun Özlem Güney

Mathematics 2026, 14(7), 1203; https://doi.org/10.3390/math14071203 - 3 Apr 2026

Viewed by 319

Abstract

This paper presents a new subclass

{BS}_{k - 1}^{*}

of starlike functions with respect to symmetric points associated with a domain bounded by an epicycloid with

k - 1

cusps. First, we derive bounds for the first five Taylor coefficients of [...] Read more.

This paper presents a new subclass

{BS}_{k - 1}^{*}

of starlike functions with respect to symmetric points associated with a domain bounded by an epicycloid with

k - 1

cusps. First, we derive bounds for the first five Taylor coefficients of functions in this subclass and obtain the first three coefficients of the corresponding logarithmic function. Moreover, for some special values, upper and lower bounds are established for several important functionals and determinants associated with the coefficients of functions in this subclass. Full article

(This article belongs to the Section C: Mathematical Analysis)

23 pages, 375 KB

Open AccessArticle

Sharp Bounds of Hermitian Toeplitz Determinants for Bounded Turning Functions

by Wahid Ullah, Rabia Fayyaz, Daniel Breaz and Luminiţa-Ioana Cotîrlă

Symmetry 2025, 17(3), 407; https://doi.org/10.3390/sym17030407 - 8 Mar 2025

Viewed by 1619

Abstract

Hermitian Toeplitz determinants are used in multiple disciplines, including functional analysis, applied mathematics, physics, and engineering sciences. We calculate the sharp upper and lower bounds on the fourth-order Hermitian Toeplitz determinant for the subclass of bounded turning functions associated with the nephroid function [...] Read more.

R_{n}

. A nephroid function is associated with the geometric shape of a nephroid (a kidney-shaped curve) and refers to a specific type of epicycloid with two cusps. In geometric function theory, a bounded turning function is an analytic function whose derivative has a positive real part, ensuring that its tangent vector does not turn too sharply at any point. Full article

(This article belongs to the Special Issue Symmetry and Its Applications in Complex Analysis by the Means of Special Functions)

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17 pages, 319 KB

Open AccessArticle

Bounds for Hermitian Toeplitz and Hankel Determinants for a Certain Subclass of Analytic Functions Related to the Sine Function

by Thatamsetty Thulasiram, Sekar Kalaiselvan, Daniel Breaz, Kuppuswamy Suchithra and Thirumalai Vinjimur Sudharsan

Symmetry 2025, 17(3), 362; https://doi.org/10.3390/sym17030362 - 27 Feb 2025

Viewed by 1134

Abstract

This study of Hankel and Hermitian Toeplitz determinants is one of the major areas of interest in Geometric function theory and has wide applications in the areas of signal processing and Applied Mathematics. In our present investigations, we define a new subclass of [...] Read more.

H (λ)

(λ \geq 0)

, defined using a subordination relation with the sine function

K (z) = 1 + s i n z

. For the class

H (λ)

, coefficient estimates, upper and lower bounds for the Hermitian Toeplitz determinants of second and third order are found. In addition, estimates are provided for the second and third-order Hankel determinants for the class

H (λ)

. Full article

(This article belongs to the Section Mathematics)

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13 pages, 286 KB

Open AccessArticle

Hankel Determinants of Normalized Analytic Functions Associated with Hyperbolic Secant Function

by Sushil Kumar, Daniel Breaz, Luminita-Ioana Cotîrlă and Asena Çetinkaya

Symmetry 2024, 16(10), 1303; https://doi.org/10.3390/sym16101303 - 3 Oct 2024

Cited by 6 | Viewed by 1858

Abstract

In this paper, we consider a subclass of normalized analytic functions associated with the hyperbolic secant function. We compute the sharp bounds on third- and fourth-order Hermitian–Toeplitz determinants for functions in this class. Moreover, we determine the bounds on second- and third-order Hankel determinants, as well as on the generalized Zalcman conjecture. We examine a Briot–Bouquet-type differential subordination involving the Bernardi integral operator. Finally, we obtain a univalent solution to the Briot–Bouquet differential equation, and discuss the majorization property for such function classes. Full article

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

7 pages, 248 KB

Open AccessArticle

The Third-Order Hermitian Toeplitz Determinant for Alpha-Convex Functions

by Anna Dobosz

Symmetry 2021, 13(7), 1274; https://doi.org/10.3390/sym13071274 - 16 Jul 2021

Cited by 3 | Viewed by 2471

Abstract

Sharp lower and upper bounds of the second- and third-order Hermitian Toeplitz determinants for the class of

α

-convex functions were found. The symmetry properties of the arithmetic mean underlying the definition of

α

-convexity and the symmetry properties of Hermitian matrices were [...] Read more.

Sharp lower and upper bounds of the second- and third-order Hermitian Toeplitz determinants for the class of

α

-convex functions were found. The symmetry properties of the arithmetic mean underlying the definition of

α

-convexity and the symmetry properties of Hermitian matrices were used. Full article

(This article belongs to the Special Issue Special Functions and Polynomials)

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