A DEVELOPMENT ON APPROXIMATION BY MONOTONE SEQUENCES OF POLYNOMIALS

Recently people proved that every f∈C[0, 1] can be uniformly approximatedby polynomial sequences {P_n}, {Q_n} such for any x∈[0,1] and n=1,2,…that Q_n(x)相似文献   

ON SATURATION FOR A SPLINE APPROXIMATION

We obtain a saturation theorem for a wavelet operator which is constructed by B-splins function.     

ON COPOSITIVE APPROXIMATION

The present note investigates the divergence phenomenon of copositive approximation by poiynomials inL'spaces. We show that the Jackson type estimates cannot hold, in general, for moduli of smoothness ofhigher degree.     

ON ANALYTIC CONTINUATION OF A REAL APPROXIMATION FORMULA

In this paper, we try to discuss the relation between the realapproximation and the complex approximation, precisely, we havegiven an analytic continuation of a real approximation formula.     

ON DIOPHANTINE APPROXIMATION AND APPROXIMATE ANALYSIS(Ⅱ)

<正> 1.INTRODUCTIONLet a and C be two positive constants.Let E_s~a(C) be the class of functions of G_s:∫(x)～∑C(m)e~(2πi(m,x)),Where the Fourier coefficients satisfy     

ON BEST LOCAL APPROXIMATION

The purpose of this paper is to introduce certain aspects concerning the problem of best local approximations. Especially in multipoint best local approximation, there are many intuitively quite clear yet unsolved interesting problems. We will discuss some recent results and some unsolved problems.     

APPROXIMATION BY INTEGRAL TYPE MEYER-KONIG-ZELLER OPERATORS ON A SIMPLEX

Letbe a simplex in The integral type Meyer-Komg-Zeller operators are constructed on the simplex T, and the degree of approximation of these operators for L'-functions is obtained.     

ON VECTOR VALUED FUNCTION APPROXIMATION USING A PEAK NORM

A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.     

ON MONOTONE CONVERGENCE OF NONLINEARMULTISPLITTING RELAXATION METHODS

ＯＮＭＯＮＯＴＯＮＥＣＯＮＶＥＲＧＥＮＣＥＯＦＮＯＮＬＩＮＥＡＲＭＵＬＴＩＳＰＬＩＴＴＩＮＧＲＥＬＡＸＡＴＩＯＮＭＥＴＨＯＤＳ￥ＷＡＮＧＤＥＲＥＮ；ＢＡＩＺＨＯＮＧＺＨＩ（ＤｅｐａｚａｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈｓｌｌｇｈａｉＵｎｉｖｅ...     

ON M-IDEALS AND BEST APPROXIMATION

ＯＮＭ－ＩＤＥＡＬＳＡＮＤＢＥＳＴＡＰＰＲＯＸＩＭＡＴＩＯＮＨＡＮＤＥＧＵＡＮＧ（韩德广）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｑｕｆｕ２７３１６５，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａ...     

ON MONOTONE METHOD FOR NONLINEAR REACTION-DIFFUSION SYSTEM

If we knew the existence of upper and lower solutions u, v of a coupled reaction-diffusion system with quasi-monotone nonlinear reaction functions, then we can prove the existence of a solution ω of the same system such that u<ω相似文献   

ON A SURJECTIVITY FOR THE SUM OF TWO MAPPINGS OF MONOTONE TYPE

In this paper the sum(T+S)of two nonlinear mappings is considered,where T ismaximal monotone or generalized pseudomonotone and S is generalized pseudomonotone orof type(M).By using the concepts of T-boundedness,T-generalized pseudomonotonemappings and mappings of type T--(M) introduced by the author,it is proved that(T+S) is of type (M).A new surjectivity result for multivalued pseudo A-propermappings is given.As a consequence,it is obtained that the coercive mappings of type(M)whose effective domain contains a dense linear subspace are surjectivity. In particular,the author answers affirmatively a part of Browder's question(see[1],p.70).     

ON AN INVERSE THEOREM OF APPROXIMATION

The author gives some disagreement to the following result,which is published in [1].Let {L_n(f(}be mass-concerntative,φ_n→0+(n→∞),0<α≤2 andC~(-1)≤(φn+1)/(φn)≤C(n=1,2,…)for some constrant C>0.Then for any f∈C[-2a,2a],||L_n(f)-f||σ[-a,a]=O(φ_n~α)implies f∈Lip*α,whereLip*a={f∈C[-2a,2a]|w_2(f,δ)[-2a,2a]=O(δ~α)}.Then some similar results on C_(2π)are given,and further some results on C[-2a,2a]areestablished by adding some proper conditions.     

THE APPROXIMATION ON LOCALLY CONVEX SPACES

In this paper, we give some properties of f-approximation, f-Chebyshev centers andf-farthest points in locally convex spaces.     

WEIGHTED APPROXIMATION ON SZASZ—TYPE OPERATORS

In this paper, we use weighted modules ω(?)(f,t)w to study the pointwise approximation on Szasz-type operators, and obtain the direct and converse theorem, as well as characterizations of the pointwise approximation of Jacobi-weighted Szasz-type operators.     

RATIONAL APPROXIMATION IN L φ SPACES ON A FINITE UNION OF DISJOINT INTERVALS

ABSTRACT

In this paper we study the convergence of the best rational approximants, to a function f, respect to the Luxemburg norm on a finite union of disjoint intervals, with diameters shrinking to zero. This work extends previous results on L^p spaces. We also prove existence of best local quasi-rational approximants on a finite point set.     

ON APPROXIMATION OF OPTIMAL STOPPING OF BMESIAN SEQUENTIAL TEST FOR A NORMAL MEAN

ＯＮＡＰＰＲＯＸＩＭＡＴＩＯＮＯＦＯＰＴＩＭＡＬＳＴＯＰＰＩＮＧＯＦＢＭＥＳＩＡＮＳＥＱＵＥＮＴＩＡＬＴＥＳＴＦＯＲＡＮＯＲＭＡＬＭＥＡＮ￥ＷＡＮＦＡＮＧＨＵＡＮ；ＡＮＤＷＵＸＩＺＨＩＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｐｒｅｓｅｎｔａｓｉ...     

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.     

ON THE DEGREE OF APPROXIMATION BY WAVELET EXPANSIONS

In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x) ∈ L2 continuous in a finite interval (a,b) which is much superior to those of approximation by polynomial operators and by expansions of classical orthogonal series.     

SOME CONVERSE RESULTS ON ONESIDED APPROXIMATION ： JUSTIFICATIONS

The present paper deals with best onesided approximation rate in Lp spaces ^~En（f）Lp of f∈C2π.Although it is clear that the estimate ^~E(f)Lp≤C‖f‖Lp cannot be correct for all f∈L^p2π in case p＜∞, the question whether ~En(f)Lp≤Cω(f,n^-l)Lp or ^~En(f)Lp≤CEn(f)Lp holds for f∈ C2π remains totally untouched.Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.