‎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.  

‎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.

The purpose of this note is two-fold. First we present evaluations of Hankel determinants of sequences of combinatorial interest related to partitions and permutations. Many such computations have been carried out by Radoux in his sequence of papers [2]–[5]. His proof methods include using a functional identity due to Sylvester and factoring the Hankel matrix. Second, unlike Radoux, we instead ...

In our present study, two subclasses of starlike functions which are symmetric about the origin considered. These classes defined with use sigmoid function and trigonometric function, respectively. We estimate first four initial logarithmic coefficients, Zalcman functional, Fekete–Szegö bounds second-order Hankel determinants coefficients for class Sseg* improve obtained existing determinant se...

Let be the class of functions which are analytic in open unit disk and having form . Denote to for all that univalent Then, let denote bi-univalent In this paper, we obtain second Hankel determinant certain classes function defined by subordinations particular, determine initial coefficients obtained upper bound functional

In this paper, we consider a subclass SQ of normalized analytic functions f satisfying ℜf′(z)>1/2. For the in class SQ, determine upper bounds for number coefficient estimates, among which are initial coefficients, second Hankel determinant, and Zalcman functional. Upper estimates higher-order Schwarzian derivatives also obtained.

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.

In numerous geometric and physical applications of complex analysis, estimating the sharp bounds coefficient-related problems univalent functions is very important due to fact that these coefficients describe core inherent properties conformal maps. The primary goal this paper was calculate estimates initial some their combinations (the Hankel determinants, Zalcman’s functional, etc.) for class...

In this paper, we develop three essential ingredients of an algebraic structure theory of nite block Hankel matrices. The development centers around a transformation of block Hankel matrices, rst introduced by Fischer and Frobenius for scalar Hankel matrices. We prove three results: First, Iohvidov's fundamental notion of the characteristic of a Hankel matrix is extended to the block matrix cas...