Coefficient Problems for a Class of Univalent Functions

Tang, Huo; Li, Zongtao; Xu, Qingbing; Ao, En

doi:10.3390/math11081835

Cited by 2 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…then the analytic characterization of the limaçon domain L s (D) is given by the inclusion relation (see [13] inclusions (9) and (10))…”

Section: Introductionmentioning

confidence: 99%

Symmetric Toeplitz Determinants for Classes Defined by Post Quantum Operators Subordinated to the Limaçon Function

Sangarambadi Padmanabhan,

Sudharsan,

Bulboacă

2024

Stud. Univ. Babes-Bolyai Math.

View full text Add to dashboard Cite

The present extensive study is focused to find estimates for the upper bounds of the Toeplitz determinants. The logarithmic coefficients of univalent functions play an important role in different estimates in the theory of univalent functions, and in the this paper we derive the estimates of Toeplitz determinants and Toeplitz determinants of the logarithmic coefficients for the subclasses Ls𝑆𝑝𝑞 L𝑠C𝑝𝑞 and LsS𝑝𝑞 ∩ S, L𝑠𝐶𝑝𝑞 ∩ S, 0 q≤p≤10 𝑞≤𝑝≤1, defined by post quantum operators, which map the open unit disc 𝐷 onto the domain bounded by the limaçon curve defined by ∂Ds:={u+iv∈C:(u−1)2+v2−s4.2=4s2(u−1+s2)2+v2.}, where s∈−1,1.∖{0}. Keywords: Limaçon domain, subordination, (p, q)–derivative, Toeplitz and Hankel determinants, symmetric Toeplitz determinant, logarithmic coefficients, starlike functions with respect to symmetric points.

show abstract

“…then the analytic characterization of the limaçon domain L s (D) is given by the inclusion relation (see [13] inclusions (9) and (10))…”

Section: Introductionmentioning

confidence: 99%

Symmetric Toeplitz Determinants for Classes Defined by Post Quantum Operators Subordinated to the Limaçon Function

Sangarambadi Padmanabhan,

Sudharsan,

Bulboacă

2024

Stud. Univ. Babes-Bolyai Math.

View full text Add to dashboard Cite

show abstract

Inverse logarithmic coefficient bounds for starlike functions subordinated to the exponential functions

Shi,

Abbas,

Raza

et al. 2024

J Inequal Appl

View full text Add to dashboard Cite

In recent years, many subclasses of univalent functions, directly or not directly related to the exponential functions, have been introduced and studied. In this paper, we consider the class of $\mathcal{S}^{\ast}_{e}$ S e ∗ for which $zf^{\prime}(z)/f(z)$ z f ′ ( z ) / f ( z ) is subordinate to $e^{z}$ e z in the open unit disk. The classic concept of Hankel determinant is generalized by replacing the inverse logarithmic coefficient of functions belonging to certain subclasses of univalent functions. In particular, we obtain the best possible bounds for the second Hankel determinant of logarithmic coefficients of inverse starlike functions subordinated to exponential functions. This work may inspire to pay more attention to the coefficient properties with respect to the inverse functions of various classes of univalent functions.

show abstract

Coefficient Problems for a Class of Univalent Functions

Cited by 2 publications

References 15 publications

Symmetric Toeplitz Determinants for Classes Defined by Post Quantum Operators Subordinated to the Limaçon Function

Symmetric Toeplitz Determinants for Classes Defined by Post Quantum Operators Subordinated to the Limaçon Function

Inverse logarithmic coefficient bounds for starlike functions subordinated to the exponential functions

Contact Info

Product

Resources

About