涉及齐次微分多项式的亚纯函数的唯一性

本文证明了下述定理：设f是复平面内一个非常数的亚纯函数，H(f,f′,…，f^m)表示关于f的次数m≥2，的齐次微分多项式，再设a和b是f的两个判别的有穷小函数，如果f^m=a=(f,f′，…f^m)=a并且f^m=b=H(f,f′，…f^m)=b,那么f^m=H(f,f′,…f^m)，上述定理改进了L.A.Rubel and C.C.Yang[1],顾永兴[2]和方明亮[3]中的有关结果。     

TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES

In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequalities, we extends this result to W 1 H inequalities.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa^[6], G. Gundersen^[7] and J.K. Langley^[8], Li Chun-hong^[11].     

Banach空间中一类C~∞函数芽等价的条件(英文)

In this paper,we prove the converse of gem is right equivalent is also true in[1] and[2],obtain the necessary and sufficient conditions of equivalence of a class gems of C∞ function on Banach spaces.     

COMPOSITION OPERATORS BETWEEN SOME WEIGHTED HARDY SPACES

Let D be the unit disc and H(D) be the set of all analytic functions on D. In [2], C. Cowen defined a space H = f ∈ H(D) : f(z) =sum from k=o to ∞ ak(z + 1)k, z∈ D, ‖f‖2 = sum from k=o to ∞ |ak|24k < ∞In this article, the authors consider the similar Hardy spaces with arbitrary weights and discuss some properties of them. Boundedness and compactness of composition operators between such spaces are also studied.     

Some new classes of Kadison-Singer lattices in Hilbert spaces

Let N be a maximal and discrete nest on a separable Hilbert space H,E the projection from H onto the subspace[C]spanned by a particular separating vector for N′and Q the projection from K=H⊕H onto the closed subspace{(,):∈H}.Let L be the closed lattice in the strong operator topology generated by the projections(E 00 0),{(E 00 0):E∈N}and Q.We show that L is a Kadison-Singer lattice with trivial commutant,i.e.,L′=CI.Furthermore,we similarly construct some Kadison-Singer lattices in the matrix algebras M2n(C)and M2n.1(C).     

TWO MEROMORPHIC FUNCTIONS SHARE SOME PAIRS OF SMALL FUNCTIONS WITH TRUNCATED MULTIPLICITIES

Using the techniques proposed in [3], we prove that two nonconstant meromorphic functions f and g on C must be linked by a quasi-Mbius transformation if they share some pairs of small functions with more precise truncated multiplicities, which improve and extend the results of Duc Quang Si.     

ON THE PROBLEMS OF PREVENTING THE BLOWING UP OF THE SOLUTIONS FOR SEMILINEAR PARABOLIC EQUATIONS

§ 1 Introduction The investigating of the existence of globally smooth solutions or the formation of singularities of the solutions for semilinear parabolic equations is of much importance in the theory of partial differential equation as well as in the application. The blowing up of the solutions is an interesting phenomenon and has been pointed out by many authors in various cases, such as by S. Kaplan [1], C. V. pao[2], H. Kawarada[3]etc. In[4], Chen studied the problem of     

C_(αβ) Classification of Analytic Toeplitz Operators

Let H be a separable Hilbert space and L(H) the set of all bounded linear operatorson H .A∈ L (H ) is said to be a contraction if‖ A‖≤ 1 .In [1 ] Sz-Nagy and Foiasintroduced the notion of the class Cαβ of contractions on H as follows:　Definition1　 Let T∈L(H) be a contraction.WriteT∈C0 .,　　 if h∈H,‖Tnh‖→ 0 ,as n→∞ ;T∈C1· ,　　if h∈H,h≠ 0 ,‖ Tnh‖\→ 0 ,as n→∞ ;T∈C· 0 ,　　if h∈H,‖ T* nh‖→ 0 ,as n→∞ ;T∈C· 1 ,　　if h∈H,h≠ 0 ,‖ T* nh‖\→ 0 …     

On Meromorphic Starlike Multivalent Functions

In this paper we introduce and study some new subclasses of meromorphic starlike multivalentfunctions.Inclusion relations are established,Integral transforms of functions in these classes are alsoconsidered.In particular,our results include or improve several results due to Mogra et al.[2],Mogra[3],Goel and Sohe[4]and Bajpai[5].     

Uniqueness and value-sharing of entire functions

In this paper, we study the uniqueness problems on entire functions sharing one value with the same multiplicities. We generalize and unify some previous results of Fang and Hua [M.L. Fang, X.H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly 13 (1) (1996) 44-48], Yang and Hua [C.C. Yang, X.H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (2) (1997) 395-406] and Fang [M.L. Fang, Uniqueness and value-sharing of entire functions, Comput. Math. Appl. 44 (2002) 828-831].     

Value sharing results for shifts of meromorphic functions

In this paper, we deal with the value distribution of difference products of entire functions, and present some result on two difference products of entire functions sharing one value with the same multiplicities. The research findings also include an analogue for shift of a well-known conjecture by Brück. Our theorems improve the results of I. Laine and C.C. Yang [I. Laine, C.C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007) 148-151], K. Liu and L.Z. Yang [K. Liu, L.Z. Yang, Value distribution of the difference operator, Arch. Math. 92 (2009) 270-278], and J. Heittokangas et al. [J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, J.L. Zhang, Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009) 352-363]. Moreover, we show by illustrating a number of examples that our results are best possible in certain senses.     

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM, FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS, AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article,we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems,the set of common fixed point for a family of infinite...     

一类周期小波的局部性质

在文献[1]中,陈翰麟等构造了一类具有很好性质的周期小波．我们在这篇论文中进一步研究了该类周期小波,证明了它们在一个周期内具有局部性质．     

On a question of Gross

Using the notion of weighted sharing of sets we prove two uniqueness theorems which improve the results proved by Fang and Qiu [H. Qiu, M. Fang, A unicity theorem for meromorphic functions, Bull. Malaysian Math. Sci. Soc. 25 (2002) 31-38], Lahiri and Banerjee [I. Lahiri, A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J. 44 (2004) 575-584] and Yi and Lin [H.X. Yi, W.C. Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad. Ser. A 80 (2004) 136-140] and thus provide an answer to the question of Gross [F. Gross, Factorization of meromorphic functions and some open problems, in: Proc. Conf. Univ. Kentucky, Lexington, KY, 1976, in: Lecture Notes in Math., vol. 599, Springer, Berlin, 1977, pp. 51-69], under a weaker hypothesis.     

IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem

We develop the Hutchinson-Barnsley theory for finite families of mappings on a metric space endowed with a directed graph. In particular, our results subsume a classical theorem of J.E. Hutchinson [J.E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981) 713-747] on the existence of an invariant set for an iterated function system of Banach contractions, and a theorem of L. Máté [L. Máté, The Hutchinson-Barnsley theory for certain non-contraction mappings, Period. Math. Hungar. 27 (1993) 21-33] concerning finite families of locally uniformly contractions introduced by Edelstein. Also, they generalize recent fixed point theorems of A.C.M. Ran and M.C.B. Reurings [A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto and R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], and A. Petru?el and I.A. Rus [A. Petru?el, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] for contractive mappings on an ordered metric space. As an application, we obtain a theorem on the convergence of infinite products of linear operators on an arbitrary Banach space. This result yields new generalizations of the Kelisky-Rivlin theorem on iterates of the Bernstein operators on the space C[0,1] as well as its extensions given recently by H. Oruç and N. Tuncer [H. Oruç, N. Tuncer, On the convergence and iterates of q-Bernstein polynomials, J. Approx. Theory 117 (2002) 301-313], and H. Gonska and P. Pi?ul [H. Gonska, P. Pi?ul, Remarks on an article of J.P. King, Comment. Math. Univ. Carolin. 46 (2005) 645-652].     

A modified halpern-type iteration algorithm for totally quasi-?-asymptotically nonexpansive mappings with applications

The purpose of this article is to modify the Halpern-type iteration algorithm for total quasi-?-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results of [X.L. Qin, Y.J. Cho, S.M. Kang, H. Y. Zhou, Convergence of a modified Halpern-type iterative algorithm for quasi-?-nonexpansive mappings, Appl. Math. Lett. 22 (2009) 1051-1055], [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364-2371], [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890-3906], [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and others.     

Parametrization of minimal rank block Hankel matrix extensions and minimal partial realizations

A parametrization of allm-rowsn-columns extensions of block Hankel matrices with minimal rank is presented. As a particular case, a new parametrization of the minimal partial realizations of a sequence of blocks is given. In this way results of O.H. Bosgra [2], I. Gohberg/M.A. Kaashoek/L. Lerer [3], and H. Woerdeman [13] are extended.     

G-集分次模与Morita Context

对任意群Ｇ， Ｈ≤Ｇ，［１］研究了Ｇ－分次环Ｒ与有限可迁Ｇ－集的ｓｍａｓｈ积.在本文中我们对任意可迁Ｇ－集，讨论了一个关于Ｒ（Ｈ）与ｓｍａｓｈ积Ｒ＃Ｇ／Ｈ的Ｍｏｒｉｔａ ｃｏｎｔｅｘｔ，从而推广了［２］，［３］，［４］给出的关于Ｇ－分次环及其与群Ｇ的ｓｍａｓｈ积的一些重要结果．