Third-Order Hankel and Toeplitz Determinants for Starlike Functions Connected with the Sine Function

Hai-Yan Zhang, Rekha Srivastava and Huo Tang
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Hai-Yan Zhang: School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China
Rekha Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Huo Tang: School of Mathematics and Statistics, Chifeng University, Chifeng 024000, China

Mathematics, 2019, vol. 7, issue 5, 1-10

Abstract: Let S s * be the class of normalized functions f defined in the open unit disk D = { z : | z | < 1 } such that the quantity z f ′ ( z ) f ( z ) lies in an eight-shaped region in the right-half plane and satisfying the condition z f ′ ( z ) f ( z ) ? 1 + sin z ( z ∈ D ) . In this paper, we aim to investigate the third-order Hankel determinant H 3 ( 1 ) and Toeplitz determinant T 3 ( 2 ) for this function class S s * associated with sine function and obtain the upper bounds of the determinants H 3 ( 1 ) and T 3 ( 2 ) .

Keywords: starlike function; Toeplitz determinant; Hankel determinant; sine function; upper bound (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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