Some coefficient inequalities related to the Hankel determinant for strongly starlike functions of order alpha

Abstract

Abstract. In the present paper, the estimate of the Hankel determinantMathematics subject classification (2010): 30C45. Keywords and phrases: Univalent functions, strongly starlike functions of order alpha, Hankel determinant. R E F E R E N C E S[1] R. M. ALI, V. SINGH, On the fourth and fifth coefficients of strongly starlike functions, Results in Math.

The Bound of the Hankel Determinant of the Third Kind for Starlike Functions

“…where the function is defined by (2.6). Thus the function [1,4] t →F 2 (t, •) is decreasing, and therefore we havẽ…”

“…For fixed q and n the growth problem can be reduced to an estimate of the Hankel determinant for the selected subclasses of A. Recently many authors examined the Hankel determinant H 2,2 ( f ) = a 2 a 4 − a 2 3 of order 2 (see, e.g., [3,4,6,8,12]). Note also that H 2,1 ( f ) = a 3 − a 2 2 .…”

“…t, x) ≤F 2 (1, x) = 9 56 + 85x + 17x 2 − 71x 3 + 5x4 < 1024, x ∈ [0, 1]. (2.17)Indeed, the last inequality is true since, as easy to verify the inequality−520 + 765x + 153x 2 − 639x 3 + 45x 4 < 0, x ∈ [0, 1],holds.…”

Third Hankel Determinant for A Class of Functions with Respect to Symmetric Points Associated with Exponential Function

“…Babalola [4] was the first person to study the upper bound of H 3 (1) for subclasses of S. Interested readers can see the work carried by several researchers like Vamshee Krishna et al ( [45], [46]), Prajapat et al ( [32], [33]),Altinkaya and Yalcin [3],Cho et al [8], lecko et al [19], Kowalczyk et al [17],Mohd Narzan et al [27]. Mendiratta et al [26] introduced and studied the class of starlike functions S * e = S * (e z ) defined by…”

On Hankel Determinant $${{\varvec{H}}}_\mathbf{2}{} \mathbf{(3)}$$ H 2 ( 3 ) for Univalent Functions

“…In recent years many mathematicians have investigated Hankel determinants for various classes of functions contained in A. These studies focus on the main subclasses of class S consisting of univalent functions (see, [1,3,[8][9][10][14][15][16]21,22,24,25]). A few papers are devoted to some subclasses of S σ of bi-univalent functions (see, [4,17]).…”