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.

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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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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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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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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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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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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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.

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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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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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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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.

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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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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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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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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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.