The purpose of the present paper is to investigate some inclusion properties of certain classes of meromorphic functions associated with a family of linear operators, which are defined by means of the Hadamard product or convolution . Some invariant properties under convolution are also considered for the classes presented here. The results presented here include several previous known results ...

This paper aims to provide sufficient conditions for starlikeness and convexity of Hadamard product (convolution) certain multivalent analytic functions with positive real parts. Moreover, the a integral operator other convolution results are also considered.

In this paper, we establish some results concerning the Hadamard product of certain meromorphic p-valent starlike and meromorphic p-valent convex functions analogous to those obtained by Vinod Kumar (J. Math. Anal. Appl. 113(1986), 230-234) and M. L. Mogra (Tamkang J. Math. 25(1994), no. 2, 157-162).

Recently, K.M.R. Audenaert (2010), and R.A. Horn and F. Zhang (2010) proved inequalities between the spectral radius of Hadamard products of finite nonnegative matrices and the spectral radius of their ordinary matrix product. We will prove these inequalities in such a way that they extend to infinite nonnegative matrices A and B that define bounded operators on the classical sequence spaces lp.

Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.

Proof. One can relate the singular values of the Hadamard product Z 2 to those of the Kronecker product Z ⊗ Z. In particular, as Z Z can be obtain from Z ⊗ Z by deleting some rows and columns, Lemma A.1 tells us that σmin(Z Z) ≥ σmin(Z ⊗ Z) and σmax(Z Z) ≤ σmax(Z ⊗ Z). Then the lemma follows as the Kronecker product Z⊗Z is known to have the property that σmin(Z⊗ Z) = (σmin(Z)) 2 and σmax(Z ⊗ Z)...

Let’s setup one useful form of tensor notation, which incorporates the matrix and inner product, the outer product, the Hadamard (MATLAB .* or ◦) product diag and diag−1. These will be denoted using different combinations of pairs of up-stairs and down-stairs indices. If we have only 2 order tensors (and lower) we want to be able to easily convert the result into matrix representation. We have ...

Let I be any index set. We consider the Banach algebra Ce + l(I) with the Hadamard product, and prove that its Bass and topological stable ranks are both equal to 1. We also characterize divisors, maximal ideals, closed ideals and closed principal ideals. For I = N we also characterize all prime z-ideals in this Banach algebra.

In this paper we extend some estimates of the right hand side of a Hermite-Hadamard type inequality for the product two differentiable functions whose derivatives absolute values are convex. Some natural applications to special weighted means of real numbers are given. Finally, an error estimate for the Simpson’s formula is also addressed.