On Converse Theorem of Best Approximation by Polynomials in Bergman Spaces H_q^p(p>0,q>1)

A Bernstein type theorem and a converse theorem of best approximation by polynomials in Bergman spaces Hq^p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.

A Converse Theorem for Split SO_(2l) over Finite Fields

We prove a converse theorem for split even special orthogonal groups over finite fields.This is the only case left on converse theorems of classical groups and the difficulty is the existence of the outer automorphism. In this paper, we develop new ideas and overcome this difficulty.

A General Converse Comparison Theorem for Backward Stochastic Differential Equation with Non-lipschitz Coefficient

In this article, we first introduce g-expectation via the solution of backward stochastic differential equation（BSDE in short） with non-Lipschitz coefficient, and give the properties of g-expectation, then we establish a general converse comparison theorem for backward stochastic differential equation with non-Lipschitz coefficient.

A Limit Theorem for Solutions of Backward Stochastic Differential Equations

A limit theorem for solutions of backward stochastic differential equations was established. It extends aresult of Briand et al.

The Conditions of Equivalence of a Class Germs of C~∞ Functions on Banach Spaces

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.

WEIGHTED L^p-APPROXIMATION BY THE MODIFIED NEVAI OPERATORS

The present paper gives a Jackson type estimate for Nevai operators under weighted L^p norm, and establishes the direct and converse theorems in some proper Besov spaces

INVARIANT REPRESENTATION FOR STOCHASTIC DIFFERENTIAL OPERATOR BY BSDES WITH UNIFORMLY CONTINUOUS COEFFICIENTS AND ITS APPLICATIONS

In this paper, we prove that a kind of second order stochastic differential op- erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated solutions of BSDEs. Moreover, we give a new proof about g-convexity.

Approximation of Generalized Bernstein Operators

This paper is devoted to study direct and converse approximation theorems of the generalized Bemstein operators Cn （f, sn,x） via so-called unified modulus ωφλ^2 （f,t）, 0 ≤ λ ≤1. We obtain main results as followsωφλ^2 （f,t）=O（t^α）←→｜Cn（f,sn,x）-f（x）｜=O（（n^-1/2δn^1-λ（x））^α）,where δn^2（x）=max{φ^2（x）,1/n} and 0〈α〈2.

Higher-order Mond-Weir converse duality in multiobjective programming involving cones

In this work, we established a converse duality theorem for higher-order Mond-Weir type multiob- jective programming involving cones. This fills some gap in recently work of Kim et al. [Kim D S, Kang H S, Lee Y J, et al. Higher order duality in inultiobjective programming with cone constraints. Optimization, 2010, 59： 29-43].

Representation Theorem for Generators of Quadratic BSDEs

In this paper, we establish a general representation theorem for generator of backward stochastic differential equation（BSDE）, whose generator has a quadratic growth in z. As some applications, we obtain a general converse comparison theorem of such quadratic BSDEs and uniqueness theorem, translation invariance for quadratic g-expectation.

Simultaneous Approximation by Modified Bernstein-Durrmeyer Operators *

The aim of the present paper is to prove direct and converse results for simultaneous approximation by modified Bernstein-Durrmeyer operators. A point-wise equivalence characterization of simultaneous approximation is obtained.

A Relationship Between the Conditional g-Evaluation System and the Generator g and Its Applications

In this paper, under the most elementary conditions on a backward stochastic differential equation （BSDE for short） introduced by Peng, a new relationship between the conditional g-evaluation system and the generator g of BSDE is obtained in the sense of ＂process＂, based on some recent results of Jiang. Moreover, as applications, two converse comparison theorems and two uniqueness theorems on the generators of BSDEs are proved.

On Nondifferentiable Higher-Order Symmetric Duality in Multiobjective Programming Involving Cones

In this paper,we point out some deficiencies in a recent paper(Lee and Kim in J.Nonlinear Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable higher-order symmetric duals multiobjective programming involving cones.