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Kinga Cichoń, Mieczysław Cichoń and Bianca Satco

Abstract

In this paper we investigate the space of regulated functions on a compact interval [0,1]. When equipped with the topology of uniform convergence this space is isometrically isomorphic to some space of continuous functions. We study some of its properties, including the characterization of the dual space, weak and strong compactness properties of sets. Finally, we investigate some compact and weakly compact operators on the space of regulated functions. The paper is complemented by an existence result for the Hammerstein-Stieltjes integral equation with regulated solutions.

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Cheng Xiong Sun

Abstract

Let k ∈ ℕ, m ∈ℕ ∪{0}, and let a(z)(≢ 0) be a holomorphic function, all zeros of a(z) have multiplicities at most m. Let ℱ be a family of meromorphic functions in D. If for each f ∈ℱ, the zeros of f have multiplicities at least k + m + 1 and all poles of f are of multiplicity at least m + 1, and for f,g ∈ℱ, ff (k)a(z) and gg (k)a(z) share 0, then ℱ is normal in D. Some examples are given to show that the conditions are best, and the result removes the condition “m is an even integer” in the result due to Sun [Kragujevac Journal of Math 38(2), 173-282, 2014].

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Mohammad Ashraf, Shakir Ali and Bilal Ahmad Wani

Abstract

Let ℌ be an in finite-dimensional complex Hilbert space and A be a standard operator algebra on ℌ which is closed under the adjoint operation. It is shown that every nonlinear *-Lie higher derivation D = {δn}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δn}gn∈N is an inner *-higher derivation.

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A. A. El-Deeb, H. A. Elsennary and Eze R. Nwaeze

Abstract

In this article, using two parameters, we obtain generalizations of a weighted Ostrowski type inequality and its companion inequalities on an arbitrary time scale for functions whose first delta derivatives are bounded. Our work unifies the continuous and discrete versions and can also be applied to the quantum calculus case.

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D. A. Mojdeh and A. S. Emadi

Abstract

Let G be a simple graph of order n. The connected domination polynomial of G is the polynomial Dc(G,x)=i=γc(G)|V(G)|dc(G,i)xi, where dc(G,i) is the number of connected dominating sets of G of size i and γc(G) is the connected domination number of G. In this paper we study Dc(G,x) of any graph. We classify many families of graphs by studying their connected domination polynomial.

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Romi Shamoyan and Seraphim Maksakov

Abstract

The survey collects many recent advances on area Nevanlinna type classes and related spaces of analytic functions in the unit disk concern- ing zero sets and factorization representations of these classes and discusses approaches, used in proofs of these results.

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George A. Anastassiou

Abstract

Here we study the approximation of functions by a great variety of Max-Product operators under differentiability. These are positive sublinear operators. Our study is based on our general results about positive sublinear operators. We produce Jackson type inequalities under initial conditions. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of a high order derivative of the function under approximation. We improve known related results which do not use smoothness of functions..

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Tuomo Kuusi, Giuseppe Mingione and Yannick Sire