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EN
We investigate Ore polynomial matrices, i. e., matrices with polynomial entries in d/dt whose coefficients are meromorphic functions in t and as such constitute a non-commutative ring. In particular, we study the properties of hyper-regularity and unimodularity of such matrices and derive conditions which make it possible to efficiently check for these characteristics. In addition, this approach enables computation of hyper-regular left and right and unimodular inverses.
EN
In this work we define a new operator using the extended generalized Sălăgean operator and extended Ruscheweyh operator. Denote by DRm,nλ the Hadamard product of the extended generalized Sălăgean operator Dmλ and extended Ruscheweyh operator Rn, given by DRm,nλ : [...] is the class of normalized analytic functions with [...]. The purpose of this paper is to introduce sufficient conditions for strong differential subordination and strong differential superordination involving the operator DRm,nλ and also to obtain sandwich-type results.
EN
In this paper using a differential operator, we define a new subclass of meromorphic functions. Sharp upper bounds for the functional […] in this class are obtained. An inclusion property is also given.
EN
In the present paper we define a new operator using the generalized Salagean operator and Ruscheweyh operator. Denote by [formula/wzór] the Hadamard product of the generalized Salagean operator [formula/wzór] and Ruscheweyh operator R(n), given by [fomula/wzór] is the class of normalized analytic functions with A1 = A. We study some differential subordinations regarding the operator [formula/wzór].
EN
The object of this paper is to derive some inclusion relations regarding a new class by using the generalized differential operator due to the authors.
6
EN
In this paper we discuss all normal extensions of a minimal operator generated by a linear multipoint differential-operator expression of first order in the Hilbert space of vector-functions on the finite interval in terms of boundary and interior point values. Later on, we investigate the structure of the spectrum, its discreteness and the asymptotic behavior of the eigenvalues at infinity for these extensions.
EN
By using a certain operator D(n), we introduce a class of holomorphic functions Mn(h), h convex function, and we obtain some subordination results. We also show that, for h(z) ≡ α, 0 ≤ α < 1 and z ∈ U, the set Mn(α) is convex and we obtain some new differential subordinations related to certain integral operators.
EN
In the present paper we define a new operator using the Salagean and Ruscheweyh operators. Denote by L(m)(α) the operator given by [wzór], where R(m)f(z) denote the Ruscheweyh derivative, S(m)f(z) is the Salagean operator and [wzór] is the class of normalized analytic functions. A certain subclass, denoted by [wzór], of analytic functions in the open unit disc is introduced by means of the new operator. By making use of the concept of differential subordination we will derive various properties and characteristics of the class [wzór]. Also, several differential subordinations are established regardind the operator L(m)(α).
EN
In this paper, we investigate the various important prop-erties and characteristics of the subclasses Sn (p, q, α, β) and Cn (p, q, α, β) of multivalent functions with negative coefficients defined by using a differential operator. We also derive many results for the modified Hadamard products of functions belongingto the classes Sn(p, q, α, β) and Cn(p, q, α, β). Finally several applications involving an integral operator and certain fractional calculus operators are also considered.
10
Content available remote On an operatorial inequality
EN
In this paper we give an operatorial inequality which is applied to find estimations for the solutions of some integral and differential systems of inequalities.
EN
In the present paper, making use of certain operators, some theorems involving inequalities on meromorphically multivalent functions in the punctured unit disk are obtained. Moreover, some of the results which are important for geometric function theory are also included.
12
Content available remote On the normality of first-order differential operators
EN
We investigate the relationship between the normality property of a first-order differential operator in a Hilbert space of vector-functions from the interval [O, 1] into a separable Hilbert space and the operator coefficients of the differential-operator expression which generates this operator.
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