较弱条件下一个全局隐函数存在性定理的证明

给出泛函分析中一元全局隐函数存在定理在较弱条件下的证明,与以前的证明相比,得到的证明层次清晰易于理解和掌握.     

关于凸函数定理的一种改进

基于变量替换,得到凸函数定理的一种改进,并能导出算术-几何加权平均值不等式的一个加强。     

Stability in the Cauchy and Morera Theorems for Holomorphic Functions and Their Spatial Analogs

Criteria are given for a mapping to have bounded distortion in terms of an integral estimate of the multiplicity function without any a priori assumption on the differential properties of the mapping. The result is most lucid and final in a sense for complex functions f:CC of one complex variable. Generalizations to multidimensional Beltrami systems are suggested.     

一个不等式的三种证明

针对某教材中关于凹函数不等式的一道证明题,分别采用单调性、泰勒公式和中值定理给出三种证明方法,旨在帮助学生拓展其思维广度,培养其综合能力,提高其数学素质．     

A General Fredholm Theory II: Implicit Function Theorems

This is the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. In general, these spaces are not locally homeomorphic to open sets in Banach spaces. The current paper develops the Fredholm theory in M-polyfold bundles. It consists of a transversality and a perturbation theory. In upcoming papers the generalized Fredholm theory will be applied to the Floer Theory, the Gromov–Witten Theory and the Symplectic Field Theory H.H.’s research partially supported by NSF grant DMS-0603957. K.W.’s research partially supported by NSF grant DMS-0606588.     

凸函数的双参数平均不等式的新证明

利用 Tchebycheff积分不等式和积分形式的 Cauchy中值定理证明了下列结论 :设 f(x)是 [a,b]上的正连续函数 ,且在 (a,b)内可微 ,若 f′(x)单调递增 ,则对任意的 p,q,有 Mp,q(f) 相似文献   

Covering of nonlinear maps on a cone in neighborhoods of irregular points

Inverse function theorems for smooth nonlinear maps defined on convex cones in Banach spaces in a neighborhood of an irregular point are considered. The corresponding covering theorem is proved. The proofs are based on a Banach open mapping theorem for convex cones in Banach spaces, which is also proved in the paper. Sufficient conditions for tangency to the zero set of a nonlinear map without a priori regularity assumptions are obtained.Translated from Matematicheskie Zametki, vol. 77, no. 4, 2005, pp. 483–497.Original Russian Text Copyright © 2005 by A. V. Arutyunov.This revised version was published online in April 2005 with a corrected issue number.     

Metric regularity and quantitative stability in stochastic programs with probabilistic constraints

Received January 24, 1996 / Revised version received December 24, 1997 Published online October 21, 1998