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EN
This paper deals with the growth of solutions of a class of higher order linear differential equations f(k)+Ak-1(z)f(k-1)+ … +A1(z)f’+A0(z)f=0; k≥2 when most coefficients Aj (z) (j = 0, ..., k-1) have the same ρϕ-order with each other. By using the concept of τϕ-type, we obtain some results which indicate growth estimate of every non-trivial entire solution of the above equations by the growth estimate of the coefficient A0 (z). We improve and generalize some recent results due to Chyzhykov-Semochko and the author.
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
We consider a bounded linear operator A in a Hilbert space with a Hilbert-Schmidt Hermitian component (A−A*)/2i. A sharp norm estimate is established for functions of A nonregular on the convex hull of the spectrum. The logarithm, fractional powers and meromorphic functions of operators are examples of such functions. Our results are based on the existence of a sequence An(n = 1, 2,...) of finite dimensional operators strongly converging to A, whose spectra belongs to the spectrum of A. Besides, it is shown that the resolvents and holomorphic functions of An strongly converge to the resolvent and corresponding function of A.
EN
Let f be a meromorphic function in the unit disc and (aν)kν=1 a set of distinct meromorphic functions small with respect to f. An analogue of the second main theorem for f and (aν)kν=1 is given. Upper limits for the sum of defects of an admissible meromorphic function and an admissible holomorphic function follow. For meromorphic and holomorphic functions in the unit disc and their small functions the analogues of Ullrich's theorem are presented.
5
Content available remote On an open problem of Xiao-Bin Zhang and Jun-Feng Xu
EN
The purpose of the paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [19]. We also solve an open problem as posed in the last section of [19].
EN
In the present paper we define some classes of meromorphic functions with fixed argument of coefficients. Next we obtain coefficient estimates, distortion theorems, integral means inequalities, the radii of convexity and starlikeness and convolution properties for the defined class of functions.
7
Content available remote Partial sums of a certain harmonic univalent meromorphic functions
EN
In the present paper we determine sharp lower bounds of the real part of the ratios of harmonic univalent meromorphic functions to their sequences of partial sums [...].
8
Content available remote Non linear differential polynomials sharing fixed points with finite weights
EN
We employ the notion of weighted sharing to investigate the uniqueness of meromorphic functions when two nonlinear differential polynomials share fixed points. The results of the paper improve and generalize the recent results due to Xu–Lu–Yi [10].
9
Content available remote On meromorphic multivalent functions defined with the use of linear operator
EN
In the present paper we introduce two classes of meromorphically multivalent functions and application of linear operators on these classes. We study various properties and coefficients bounds, the concept of neighbourhood also investigated.
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
The main object of the present paper is to investigate several results of certain differential operators which were recently introduced and (or) studied in a series of papers by Chen et et al. [1-3], Irmak et al. [8, 10, 11], Dziok et al. [5, 6] and Liu et al. [14]. In addition, some applications of our results involving certain differential inequalities of multivalently analytic and (or) multivalently raeromorphic functions are given. Our certain results also include some recent results in [5, 6, 9, 11, 12].
EN
In this paper we introduce and study two subclasses (Rn,p(α, A, B)) and Sn,p(α, A, B)) of meromorphic p-valent functions of order α (0 ≤ α < p) defined by certain linear operator. We investigate the various important properties and characteristics of these subclasses. Some properties of neighborhoods of functions in these subclasses are investigated. Also we derive many interesting results for the Hadamard products of functions belonging to the class Sn,p(α, A, B).
13
Content available remote Non linear differential polynomials sharing one value
EN
We prove three uniqueness theorems concerning non linear dierential polynomials which will improve and supplement some earlier results given by Yang and Hua, Lahiri.
14
Content available remote Differential polynomials and normality
EN
We prove some normality criteria for a family of meromorphic functions which improve and suppliment some earlier results.
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