We introduce a new subfamily of holomorphic functions and attempt to estimate an upper bound for the Hankel determinant second third kind normalized regular mapping f, member this class.

Correspondence: homidan@kfupm. edu.sa Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, P. O. Box 119, Saudi Arabia Abstract Hankel operators and Hankel transforms are required in a number of applications. This article proves a number of theorems that efficiently and accurately approximates a function using Hankel transforms and Hankel sum....

In this paper we determine the growth rate of the second Hankel determinant of an areally mean p-valent function. This result both extends and unifies previously known results concerning this problem.

A polynomial f in non-commuting variables is trace-positive if the trace of f(A) is positive for all tuples A of symmetric matrices of the same size. The investigation of trace-positive polynomials and of the question of when they can be written as a sum of hermitian squares and commutators of polynomials are motivated by their connection to two famous conjectures: The BMV conjecture from stati...

We discuss the Feferman-Vaught Theorem in the setting of abstract model theory for finite structures. We look at sum-like and product-like binary operations on finite structures and their Hankel matrices. We show the connection between Hankel matrices and the FefermanVaught Theorem. The largest logic known to satisfy a Feferman-Vaught Theorem for product-like operations is CFOL, first order log...

The inversion problem for square matrices having the structure of a block Hankel-like matrix is studied. Examples of such matrices in&de Hankel striped, Hankel layered, and vector Hankel matrices. It is shown that the components that both determine nonsingularity and construct the inverse of such matrices are closely related to certain matrix polynomials. These matrix polynomials are multidimen...

This paper is contributed to a fast algorithm for Hankel tensor–vector products. First, we explain the necessity of fast algorithms for Hankel and block Hankel tensor–vector products by sketching the algorithm for both one-dimensional and multi-dimensional exponential data fitting. For proposing the fast algorithm, we define and investigate a special class of Hankel tensors that can be diagonal...

The problem of finding the nearest positive semidefinite Hankel matrix of a given rank to an arbitrary matrix is considered. The problem is formulated as a nonlinear minimization problem with positive semidefinite Hankel matrix as constraints. Then an algorithm with rapid convergence is obtained by the Sequential Quadratic Programming (SQP) method. A second approach is to formulate the problem ...