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Sharp bounds on the third Hankel determinant for the Ozaki close-to-convex and convex functions.
- Source :
- Lithuanian Mathematical Journal; Oct2023, Vol. 63 Issue 4, p487-504, 18p
- Publication Year :
- 2023
-
Abstract
- Our main purpose in this paper is to obtain certain sharp estimates of the third Hankel determinant for the class ℱ of Ozaki close-to-convex functions. This class was introduced by Ozaki in 1941. Functions in ℱ are not necessarily starlike but are convex in one direction and so are close-to-convex. We prove that the sharp bounds of ℋ<subscript>3,1</subscript>(f) and ℋ<subscript>3,1</subscript>(f<superscript>−1</superscript>) for f ∈ ℱ are all equal to 1/16. We also calculate the sharp bounds of the third Hankel determinant with entry of coefficients on the inverse of convex functions. [ABSTRACT FROM AUTHOR]
- Subjects :
- CONVEX functions
HANKEL functions
INVERSE functions
UNIVALENT functions
Subjects
Details
- Language :
- English
- ISSN :
- 03631672
- Volume :
- 63
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Lithuanian Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 174919440
- Full Text :
- https://doi.org/10.1007/s10986-023-09610-2