带约束值域的L逼近

带约束值域的一致逼近已有一些研究工作,例如[1—3]。但对于带约束值域的L逼近的一般研究尚未见到。本文将讨论这个问题:第二节讨论存在性;第三节证明两个特征定理;第四节给出唯一性的两个充分条件。     

关于J.T.Lewis的一个定理

它是在这些结点上满足插值约束的逼近函数的集合.用K_1中的元素对f的逼近就是所谓带插值约束的逼近.J.T.Lewis给出了在L_1范数意义下这类逼近的一个特征定理.     

基于Lasserre松弛的紧约束多项式优化问题逼近界分析

本文研究了紧约束多项式优化问题(POP)的界.利用Lasserre提出的将原紧约束问题转化为多项式平方和(SOS)成立的条件,给出其条件推导SOS式子成立的证明.利用原有逼近界定理,将其进一步转化,获得了新的逼近界定理.新的逼近界定理较原有定理减少了参数,便于计算.     

一类非线性项带导数的p-Laplacian边值问题正解的存在性和多解性

本文研究了一类非线性项带导数的p-Laplacian算子的分数阶微分方程边值问题正解的存在性和多解性.首先,利用分数阶微分方程和边值条件给出了该边值问题的Green函数,然后利用Guo-Krasnosel’skii’s不动点定理和Leggett-Williams不动点定理得出该边值问题一个或者三个正解的存在性结论.作为应用,给出两个例子验证了结论的适用性,特别是,用迭代法进行了逼近模拟,给出解的图形.值得一提的是此文研究的微分方程的非线性项是带有Riemann-Liouville型分数阶微分.     

Bernstein算子的点态同时逼近

借助光滑模ω_φ~2(f,t)(φ是一般步权函数),研究了Bernstein算子的点态同时逼近问题,给出了Bernstein算子同时逼近的等价定理,建立了其导数与光滑函数间的关系,对以前已有的结果予以补充和完善.     

拟凸函数与切比晓夫逼近

木文第一节给出拟凸函数和显拟凸函数(explicitly quasiconvex functions)的一个新的特征;同时引进一种新的凸性——我们称它为强伪凸性,并给出它的若干重要性质.第二节讨论第一节的结果在最佳一致逼近中的应用,建立了交错定理、唯一性定理和强唯一性定理.     

集值优化问题超有效解的高阶Mond-Weir对偶

在实赋范线性空间中利用锥方向高阶广义邻接导数研究带约束的集值优化在超有效解意义下的高阶Mond-Weir对偶问题.在广义锥-凸假设下,利用锥方向高阶广义邻接导数的性质借助凸集分离定理得到了强对偶定理.利用超有效点的标量化定理得到逆对偶定理.     

集值优化问题ε-严有效解的二阶Mond-Weir对偶

在实赋范线性空间中研究带约束的集值优化在ε-严有效意义下的二阶Mond-Weir对偶问题.利用广义二阶邻接导数的性质,借助凸集分离定理得到了强对偶定理.利用ε-严有效点的性质得到了逆对偶定理.     

一类三角级数的最佳逼近度

本文在复值连续函数空间中给出一类具有O-正则变化拟单调系数之三角级数的最佳逼近度的一个完备结果.特别是第3节的定理3.2,即使在实连续函数空间中亦是一个新的结论,而且也是Xie与Zhou[6]的定理2在一个方向上的本质推广.最后,在第4节给出一个应用.     

Bernstein-Kantorovich算子导数的逼近

给出了Bernstein-Kantorovich算子的导数和光滑模之间的关系及它们的线性组合的逼近等价定理.     

Bernstein-Sikkema算子逼近

研究Ｂｅｒｎｓｔｅｉｎ－Ｓｉｋｋｅｍａ算子的逼近问题,得到强型正定理和弱型逆定理,改进了文献［１］的结果     

Note On The Utility Of A Theorem Of Leindler–Meir–Totik

Our purpose is to generalize and to extend a theorem of S. Sharma and S. K. Varma [15] concerning the order of approximation by Abel means in the Lipschitz norm. The proof is basically based on a simple extension of a general theorem of L. Leindler, A. Meir and V. Totik [6] related to approximation by finite summability methods.     

Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces

In this paper, we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove a strong convergence theorem which is connected with Combettes and Hirstoaga's result [P.L. Combettes, S.A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005) 117-136] and Wittmann's result [R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491]. Using this result, we obtain two corollaries which improve and extend their results.     

Banach空间中二阶非线性脉冲微分积分方程初值问题的整体解

通过逐步求解,应用Banach不动点定理,在较宽松的条件下,获得Banach空间中二阶非线性脉冲微分积分方程初值问题解的存在性与唯一性及解的迭代逼近.对文［1］的结果及文［2］相应于d\-0=0的结果,作了重要改进和推广.     

Lp空间Shepard算子逼近的正逆定理

本文引入了一种修正的积分型Shepard算子,建立了相应的Jackson型定理,并通过建立Bernstein型不等式,给出了算子在L[0,1]p空间中一种新的逼近阶刻画的等价形式,得到了逼近的逆定理．     

Zum Franklin—Schneiderschen Satz

In this note we shall carry on further the simultaneous approximation of a, b and exp(bloga). In a recent paper BUNDSCHUH [2] proved a theorem which appears to be a sharpening of a theorem of SCHNEIDER [10]. But there is an error in the proof. We shall show, that under a supplementary condition, the theorem of BUNDSCHUH remains valid and as well, get an improvement to this theorem. We further give some results on linear forms in logarithms of two U-numbers with algebraic coefficients.     

Approximation für Okasche Paare von Garben homogener Räume

This article brings an approximation theorem for sections of Oka pairs of sheaves of homogeneous spaces (such sheaves were introduced in [15]). Among the applications are: an Oka principle for the approximation of a generating system for a coherent analytic sheaf and an Oka principle for the approximation of a holomorphic fibre bundle with homogeneous fibre (without a structure group). Together with a homotopy theorem [15] for Oka pairs of sheaves of homogeneous spaces, a theoretical unification is thus given for various known results on the Oka principle [12,20,6,7].     

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 inBergman spaces H_q~p(p>0,q>1) are proved.Some proofs and results in [1] are in proved.     

Note On The Utility Of A Theorem Of Leindler–Meir–Totik

Our purpose is to generalize and to extend a theorem of S. Sharma and S. K. Varma [15] concerning the order of approximation by Abel means in the Lipschitz norm. The proof is basically based on a simple extension of a general theorem of L. Leindler, A. Meir and V. Totik [6] related to approximation by finite summability methods. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stability in first approximation of stochastic systems with after effect : PMM vol. 40, n 6, 1976, pp. 1116–1121

The theorem on existence of the Liapunov functionals and the theorem on stability in first approximation for a stochastic differential equation with aftereffect are proved.The suggestion of the replacement of Liapunov functions by functionals [1] in the investigation of the stability of ordinary differential equations with lag, has been widely utilized in dealing with determinate systems, as well as in the case of linear and nonlinear stochastic systems (see e. g. [2 – 11]). Results concerning the stability in the first approximation were obtained for stochastic systems in [12 – 18] and others. Use of Liapunov functionals for the differential equations with aftereffect was first encountered in [1, 19, 20] where the inversion theorems were proved and conditions for the stability in first approximation were obtained.Below a stochastic differential equation with aftereffect is investigated where the random perturbations represent an arbitrary process with independent increments.