Hadamard Product (or Convolution)

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Differential Subordination with Hadamard Product of Generalized k-Mittag-Leffler Function and a Class of Function

Differential Subordination with Hadamard Product of Generalized k-Mittag-Leffler Function and a Class of Function

In this paper we introduce Differential subordination with Hadamard Product (Convolution) of Generalized k- Mittag-Leffler function and A Class of Function in the Open Unit Disk ⅅ = 𝑧 ∈ ℂ ∶ 𝑧 < 1 , Which are expressed in terms of the A Class of Function. Some interesting special cases of our main results are also considered.

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New inequalities on eigenvalues of the Hadamard product and the Fan product of matrices

New inequalities on eigenvalues of the Hadamard product and the Fan product of matrices

In the paper, some new upper bounds for the spectral radius of the Hadamard product of nonnegative matrices, and the low bounds for the minimum eigenvalue of the Fan product of nonsingular M-matrices are given. These new bounds improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.

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The closure property of \(\mathcal{H}\) tensors under the Hadamard product

The closure property of \(\mathcal{H}\) tensors under the Hadamard product

Clearly, these interesting results are due to the special structures of H-tensors. So it is natural to consider how to preserve the structure properties under certain operations. In addition, many interesting results have been obtained for the Hadamard products involv- ing M-matrices and H-matrices []. It is natural to ask whether we can provide similar results for the tensor case. Motivated by these facts, the aim of this paper is to investigate the closure property of H-tensors under the Hadamard product.

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4. On Quasi-Hadamard Product of Certain Classes of Analytic Functions

4. On Quasi-Hadamard Product of Certain Classes of Analytic Functions

We note that, several interesting properties and characteristics of the quasi- Hadamard product of two or more functions can be found in the recent investi- gations by (for example) Raina and Bansal [7], Raina and Prajapat [8], Aouf [1], Darwish and Aouf [3], El-Ashwah and Aouf [4], and the references cited therein. In this paper, we aim at proving some new quasi-Hadamard product properties for the function classes 𝒮𝒯 𝑛 (𝛼, 𝛽). Relevant connections of the results presented

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Applications of Ruscheweyh derivatives and Hadamard product to analytic functions

Applications of Ruscheweyh derivatives and Hadamard product to analytic functions

the nth Ruscheweyh derivative of f (z) by Al-Amiri [2]. Recently, several subclasses of H have been introduced and studied by using either the Hadamard product or Ruscheweyh derivatives (see [1, 4, 7, 8], etc.). To provide a unified approach to the study of various properties of these classes, we introduce the following most general- ized subclass of H by using both the Hadamard product and Ruscheweyh derivatives.

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Some New Bounds for the Hadamard Product of a Nonsingular M-matrix and Its Inverse

Some New Bounds for the Hadamard Product of a Nonsingular M-matrix and Its Inverse

Abstract—Some new convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix and an inverse M-matrix are given. Numerical examples show that these bounds could reach the true value of the minimum eigenvalue in some cases. These bounds in this paper improve some existing ones.

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Classes of Meromorphic Functions Defined by the Hadamard Product

Classes of Meromorphic Functions Defined by the Hadamard Product

The object of the present paper is to introduce new classes of meromorphic functions with varying argument of coefficients defined by means of the Hadamard product or convolution. Several properties like the coefficients bounds, growth and distortion theorems, radii of starlikeness and convexity, and partial sums are investigated. Some consequences of the main results for well- known classes of meromorphic functions are also pointed out.

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A Proof of the Riemann Hypothesis Based on Hadamard Product

A Proof of the Riemann Hypothesis Based on Hadamard Product

The proof of the Riemann Hypothesis would unravel many of the mysteries surrounding the distribution of prime numbers, as the primes are at the heart of all encryption systems. Furthermore, the proof of the Riemann Hypothesis would as a consequence, prove many of the propositions known to be true under the Riemann Hypothesis. The proof shown in this paper was based on a basic insight into the relation of the Hadamard product expansion and the functional equation of the Riemann zeta function, which were available from Hadamard’s publication in (1893) and Riemann’s first publication in (1859). Sometimes the truth is hidden in plain sight.

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Some inequalities for the Hadamard product of an M matrix and an inverse M matrix

Some inequalities for the Hadamard product of an M matrix and an inverse M matrix

and can serve as a check of whether the solution technique for it actually resulted in valid solution. Besides, a good bound of q(A ◦ B – ) can also help us reduce the computational burden. Therefore, it is necessary to study the bound. In this paper, we present some new lower bounds of the minimum eigenvalue q(A ◦ B – ) for the Hadamard product of M-

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Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Abstract: In this paper, some mixed type bounds on the spectral radius ρ ( A ◦ B ) for the Hadamard product of two nonnegative matrices (A and B) and the minimum eigenvalue τ ( C ? D ) of the Fan product of two M-matrices (C and D) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several M-matrices is also presented:

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Hadamard product of analytic functions and some special regions and curves

Hadamard product of analytic functions and some special regions and curves

This relationship allows us to obtain several subordination results about convolution. Note that there are no assumptions about the normalization of functions. It is one of the solutions of Problem . Many of the convolution properties were studied by Ruscheweyh in [], and they have found many applications in various fields. The book [] is also an ex- cellent survey of the results. For the recent results on the Hadamard product in geometric function theory, see [–].

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Two inequalities for the Hadamard product of matrices

Two inequalities for the Hadamard product of matrices

Using a estimate on the Perron root of the nonnegative matrix in terms of paths in the associated directed graph, two new upper bounds for the Hadamard product of matrices are proposed. These bounds improve some existing results and this is shown by numerical examples.

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On A Certain Class of Multivalent Functions Defined By Hadamard Product

On A Certain Class of Multivalent Functions Defined By Hadamard Product

Owa, S., 1992. The quasi-Hadamard products of certain analytic functions, in Current Topics in Analytic Function Theory, H. M. Srivastava and S. Owa, (Editors), World Scientific Publishing Company, Singapore, New Jersey, London, and Hong Kong.

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3. Certain Coefficient Inequalities for Sakaguchi Type Functions
and Applications to Fractional Derivatives

3. Certain Coefficient Inequalities for Sakaguchi Type Functions and Applications to Fractional Derivatives

In the present paper, we obtain the Fekete-Szeg¨ o inequality for the functions in the subclass M (ϕ, λ, t). We also give application of our results to certain functions defined through convolution (or Hadamard product) and in particular, we consider the class M γ (ϕ, λ, t) defined by fractional derivatives.

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On the Connection between Kronecker and Hadamard Convolution Products of Matrices and Some Applications

On the Connection between Kronecker and Hadamard Convolution Products of Matrices and Some Applications

We are concerned with Kronecker and Hadamard convolution products and present some important connections between these two products. Further we establish some attractive inequalities for Hadamard convolution product. It is also proved that the results can be extended to the finite number of matrices, and some basic properties of matrix convolution products are also derived.

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4. Some Properties of Certain Subclasses of Multivalent
                       Functions

4. Some Properties of Certain Subclasses of Multivalent Functions

Abstract. The main purpose of the present paper is to derive such results as inclusion relationships and convolution properties for certain new subclasses of multivalent analytic functions involving the Dziok-Srivastava operator. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained.

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On the convolution product of the distributional kernel Kα,β,γ,ν

On the convolution product of the distributional kernel Kα,β,γ,ν

j=p+1 ∂ 2 /∂x j 2 ) 4 ] k , where p + q = n is the dimension of the space R n of the n-dimensional Eu- clidean space, x = (x 1 ,x 2 ,...,x n ) ∈ R n , k is a nonnegative integer, and α, β, γ, and ν are complex parameters. It is found that the existence of the convolution K α,β,γ,ν ∗ K α ,β ,γ ,ν is depending on the conditions of p and q.

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