Vanishing Theorems for p-Harmonic Forms on Submanifolds in Spheres

In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.

AN EXTENSION OF BROSOWSKI-MEINARDUS THEOREM ON INVARIANT APPROXIMATION

We obta(?) gener(?)ization of a fixed point th(?)of Dotson for nan-expansive mapptngs on star-sba p(?)sets and then(?)it to Prooe a unified Brosowski-M(?)us theorem on in(?)ariant approximatton in the setting,(?)fp-normed line(?)spaces.

FIXED POINT THEOREMS AND BEST APPROXIMATION IN CONVEX METRIC SPACES

Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.

Approximation Theorem of K.Fan for Positive Mapping and Applications

In this paper, we investigate the validity of approximation theorm of K. Fan for a demicompact 1-set-contraction map defined on a closed ball,an annulus and a sphere in cones. From this, we improve all recent results of Lin [2]. As applications of our theorems, we discuss the existence of positive solutions to twopoint boundary value-problems of differential equations in Banach space. At the same time, the recent main results of (3) established by Guo Dajun are Generalized and supplemented.

THE BEST APPROXIMATION AND COINCIDENCE THEOREMS FOR COMPOSITES OF ACYCLIC MAPPINGS

Some new coincidence theorem s involving a new class of set_valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For applications, some best approximation theorems and coincidence theorems for set-valued mappings are als o given. A number of known results in recent literature are improved and general ized by the theorems in this paper.

DIRECT LOCAL AND GLOBAL APPROXIMATION THEOREMS FOR SOME LINEAR POSITIVE OPERATORS

In this paper we establish direct local and global approximation theorems for Baskakov type operators and Szasz - Mirakjan type operators, respectively.

Pointwise Approximation Theorems for Combinations of Bernstein Polynomials with Inner Singularities

It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we give the Bernstein-Markov inequalities with step-weight functions for combinations of Bernstein polynomials with inner singularities as well as direct and inverse theorems.

SOME APPROXIMATION THEOREMS FOR MODIFIED BERNSTEIN-DURRMEYER OPERATORS

The modified Bernstein-Durrmeyer operators discussed in this paper are given by M_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt, where We will show,for 0<α<1 and 1≤p≤∞ M,f-f_p=O(n^-a)ω_Φ~2(f,t)_p=O(t^(2a)), |M_n f-f(x)|≤M(x(1-x)/n+1/_n2)~a/2ω(f,t)=O(t^a), where otherwise.

Inverse Theorem of Approximation in L_p for the Stancu Integral-type Operators on a Simplex

In this paper, the integral-type Stancu operators on a simplex is considered and its inverse theorem of approximation in Lp（1≤ p 〈＋∞）has been obtained.

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.

AN APPLICATION OF A FIXED POINT THEOREM TO BEST SIMULTANEOUS APPROXIMATION

Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.

Approximation property of partition of unity and its applications

The linear combination of certain partition of unity, subordinate to certain open covering of a compact set, is proved to be capable of approximating to a continuous function at arbitrarily precision. By using proper open covering and partition of unity, the robust nonlinear controllers and adaptive laws are designed for a class of nonlinear systems with uncertainties. The states and parameters of the closed-loop systems can be stabilized in the meaning of UUB ( uniformly ultimately bounded) via the robust nonlinear controllers and adaptive laws. Finally, an example shows the validity of method in this paper.

L^p APPROXIMATION BY GENERAL BERNSTEIN-DURRMEYER OPERATOR DEFINED ON SIMPLEX

As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.

APPROXIMATION BY GENERALIZED MKZ-OPERATORS IN POLYNOMIAL WEIGHTED SPACES

We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].

Approximation properties for the genuine modi ed Bernstein-Durrmeyer-Stancu operators

In this paper,we study on the genuine modified Bernstein-Durrmeyer-Stancu operators Gn(f,x)and investigate some approximation properties of them.Furthermore,we present a Voronovskaja type theorem for these operators.We also give some graphs and numerical examples to illustrate the convergence properties of these operators for certain functions.

On Weighted L^p-Approximation by Weighted Bernstein-Durrmeyer Operators

In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.

APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION

An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution . The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation , a piece-wise linear function , and posseses an explicit computation formula . Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function .

APPROXIMATION BY SOME OPERATORS OF SZASZ-MIRAKYAN TYPE

In this paper we give theorems on the degree of approximation of functions of one and two variables by certain operators of the Szasz-Mirakyan type.

POINTWISE SIMULTANEOUS APPROXIMATION BY LEFT GAMMA QUASI-INTERPOLANTS

Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. We consider left Gamma quasi-interpolants and give a pointwise simultaneous approximation equivalence theorem with ωφλ^2r（f,t）∞ by means of unified the classical modulus and Ditzian-Totick modulus.

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.