Sharp Bounds of Fifth Coefficient and Hermitian-Toeplitz determinants for Sakaguchi Classes

2022/10/24 by Surya Giri, Giri, Surya, S. Sivaprasad Kumar +1
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2210.13170

openalex publication_date 2022/10/24 · openalex created_date 2022/10/31 · openalex updated_date 2026/07/28

Abstract

For the classes of analytic functions f defined on the unit disk satisfying \fracz f'(z)f(z) - f(-z) \prec φ(z) and \frac(2 z f'(z))'(f(z) - f(-z))' \prec φ(z), denoted by S^*_s(φ) and C_s(φ) respectively, the sharp bound of the n^th Taylor coefficients are known for n=2, 3 and 4. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.

Related

• Hermitian Toepliz determinants for the class \S of univalent\n functions
• Toeplitz Determinants for Inverse Functions and their Logarithmic Coefficients Associated with Ma-Minda Classes
• Toeplitz Determinants in One and Higher Dimensions
• TOEPLITZ DETERMINANTS WHOSE ELEMENTS ARE THE COEFFICIENTS OF ANALYTIC AND UNIVALENT FUNCTIONS
• Toeplitz determinants whose elements are the coefficients of univalent functions