ON \(H_{3}(p)\) HANKEL DETERMINANT FOR CERTAIN SUBCLASS OF p-VALENT FUNCTIONS

Abstract

The aim of this paper is to obtain an upper bound to the H₃(p) Hankel determinant for certain subclass of p-valent functions.  To do so, we obtain best possible bounds for the functionals \(|a_{p+3} − a_{p+1}a_{p+2}|\) and \(|a_{p+2} − a_{p+1}^{2}|\), then using known upper bound for the functional \(|a_{p+1} a_{p+3} − a_{p+2}^{2}|\) we obtain the required sharp upper bound to the H₃(p) Hankel determinant.