PERTURBATIONS OF DEFINITIZABLE OPERATORS IN A SPACE WITH AN INDEFINITE METRIC

Perturbations of definitizable operators in Krein space are studied in this paper. First, the convergence of resolvents and spectral functions is discussed if a sequence of definitizable operators converges in a general sense. Second, for the operational calculus relating to continuous functions, various convergences of operator functions are studied. At last, the relation for the convergence of the sequence of resolvents and that of one-parameter unitary groups is studied. The main theorems of this paper can be regarded as the generalization of the results for self-adjoint operators in Hilbert space,     

The Stable Farkas Lemma for composite convex functions in infinite dimensional spaces

In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the composite convex functions are derived to obtain the equivalent condition of the Stable Farkas Lemma, which is formulated by using the epigraph of the conjugates for the convex functions involved and turns out to be weaker than the classic Slater condition. Moreover, we get some necessary and sufficient conditions for stable duality results of the composite convex functions and present an example to illustrate that the monotonic increasing property of the outer convex function in the objective function is essential. Our main results in this paper develop some recently results.     

Second order three-point boundary value problems in abstract spaces

In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundaryvalue problem We search for solutions of the above problem in the Banach space of continuous functions C（[O, 1], E） with the Pettis integrability assumptions imposed on $. Some classes of Pettis-integrable functions are described in the paper and exploited in the proofs of main results. We stress on a class of pseudo-solutions of considered problem. Our results extend previous results of the same type for both Bochner and Pettis integrability settings. Similar results are also proved for differential inclusions i.e. when f is a multivalued function.     

On the Coefficients of Several Classes of Bi-univalent Functions Defined by Convolution

In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a2| and |a3| for functions in these new subclasses. The results presented in this paper improve or generalize the recent works of other authors.     

ITERATIVE QUASI-LIKELIHOOD FOR SEEMINGLY UNRELATED REGRESSION SYSTEMS

In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions. Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.     

THE STABILITY AND APPROXIMATION PROPERTIES OF RITZ-VOLTERRA PROJECTION AND APPLICATION,I

The purpose of this paper is to study the stability and approximation properties of Ritz-Volterra projection. Through constructing a new type of Green functions and making use of various properties and estimates related with the functions, we prove that the Ritz-Volterra projection defined on the finite-dimensional subspace S_h of H_o~1 possesses the W_p~1-stability and the optimal approxi mation properties in W_p~1 and L_p for 2≤p≤∞. Our results, in this paper, can be applied to the finite element approximations for many evolution equations such as parabolic and hyperbolic integrodifferential equations,Sobolevequations and visco-elasticity, etc.     

A Kind of Cubic C~1—Interpolations in the n-dimensional Finite Element Method

As is well known that the multivariate spline function plays an important role in both theory and application. The paper [1]—[11] hove studied the multivariate spline functions and obtained a lot of results concerning this topic. Especially in [3], the existance theorem has been shown for the case of n-dim entional spline functions. A. Zeniek [10] and P. Alfeld [11] have established some of results about the tetrahedron partition. In this paper. we will show a kind of cubic C~1—interpolations for any n-simplicial partition in R~n. Of course, some of the subdivisions will be needed.     

UNIQUENESS AND VALUE DISTRIBUTION ON DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

In this paper, we study the value distribution question of certain difference polynomials of meromorphic functions, and investigate the uniqueness questions of meromorphic functions whose certain difference polynomials share a small functions. The results in this paper improve and extend the corresponding results in Zhang [16] and Chen [1].     

亚纯函数的n阶导数分享1值点的唯一性的一些结果

In this paper, we consider the problem of the uniqueness for meromorphic functions whose n-th derivatives share the same 1-points. The results in this paper are different from all of theorems given by H X Yi and C C Yang and other authors.     

Salagean算子定义的双单叶函数子类的系数估计

In this paper, a new subclass N_Σ~(h,p)(m, λ, μ) of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds |a_2| and |a_3| for functions of the class. Moreover, we verify Brannan and Clunie's conjecture |a_2| ≤2~(1/2)for some of our classes. The results in this paper extend many results recently researched by many authors.     

Coefficient Estimates for Certain Subclasses of Bi-Univalent Ma-Minda Mocanu-Convex Functions

In this paper, we introduce and investigate a new subclass of the function class Σ of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several(known or new) consequences of the results are also pointed out.     

预拟不变凸函数判别准则的注记

Yang et al gave some criteria of prequasi-invex functions,semistrictly prequasi-invex functions and strictly prequasi-invex functions in 2001 ,under a certain set of conditions. In this note,some of these conditions can be weakened to get the same results ,and another simplified proof for a criterion of prequasi-invex functions established under the condition of lower semicontinuity is given.     

The Refined Schwarz-Pick Estimates for Positive Real Part Holomorphic Functions in Several Complex Variables

In this article,the refined Schwarz-Pick estimates for positive real part holomorphic functions■are given,where k is a positive integer,and G is a balanced domain in complex Banach spaces.In particular,the results of first order Fréchet derivative for the above functions and higher order Frechet derivatives for positive real part holomorphic functions■are sharp for G=B,where B is the unit ball of complex Banach spaces or the unit ball of complex Hilbert spaces.Their results reduce to the classic...     

由拟从属关系定义的P叶解析函数子类的Fekete-Szeg?问题（英文）

In this paper, a new certain class of р-valent analytic functions with quasisubordination is defined and the Fekete-Szeg? problems for functions belonging to the class are derived. The results presented here provide extensions of those given in some earlier works.     

ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN

In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.     

FEKETE AND SZEG INEQUALITY FOR A SUBCLASS OF STARLIKE MAPPINGS OF ORDER αON THE BOUNDED STARLIKE CIRCULAR DOMAIN IN C~n

In this article, first, we establish the Fekete and Szeg inequality for an interesting subclass of biholomorphic functions in the open unit disk U. Second, we generalize this result to the bounded starlike circular domain in C~n. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.     

On Completeness and Minimality of Random Exponential System in a Weighted Banach Space of Functions Continuous on the Real Line

In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin's classical results.     

MBIUS INVARIANT GRADIENT AND LITTLE α-BLOCH FUNCTIONS

In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended.     

THE ANALYTICAL PROPERTIES FOR HOMOGENEOUS RANDOM TRANSITION FUNCTIONS

The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.     

函数方程的实解

In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan＇s results.