Improved Upper Bounds of the Third-Order Hankel Determinant for Ozaki Close-to-Convex Functions

Bounds for the second Hankel determinant of certain univalent functions

*Correspondence: [email protected] 1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia Full list of author information is available at the end of the article Abstract The estimates for the second Hankel determinant a2a4 – a3 of the analytic function f (z) = z + a2z + a3z + · · · , for which either zf ′(z)/f (z) or 1 + zf ′′(z)/f ′(z) is subordinate to a certai...

An upper bound to the second Hankel functional for the class of gamma-starlike functions

‎The objective of this paper is to obtain an upper bound to the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$‎ ‎for the function $f$‎, ‎belonging to the class of Gamma-starlike functions‎, ‎using Toeplitz determinants‎. ‎The result presented here include‎ ‎two known results as their special cases‎.  

Bounds of Hankel Determinant for a Class of Univalent Functions

HANKEL DETERMINANT FOR p-VALENT STARLIKE AND CONVEX FUNCTIONS OF ORDER α

The objective of this paper is to obtain an upper bound to the second Hankel determinant |ap+1ap+3 − ap+2| for p-valent starlike and convex functions of order α, using Toeplitz determinants. AMS Mathematics Subject Classification (2010): 30C45, 30C50

Second Hankel determinant for bi-starlike and bi-convex functions of order β

In this paper we obtain upper bounds for the second Hankel determinant H2(2) of the classes bi-starlike and bi-convex functions of order β, which we denote by S∗ σ(β) and Kσ(β), respectively. In particular, the estimates for the second Hankel determinat H2(2) of bi-starlike and bi-convex functions which are important subclasses of bi-univalent functions are pointed out.