一类源自二次和三次映射的混合泛函方程的模糊稳定性

研究了泛函方程2f(2x+y)+2f(2x-y)=4f(x+y)+4f(x-y)+4f(2x)+f(2y)-8f(x)-8f(y)在模糊Banach空间中的Hyers-Ulam稳定性.     

2-Banach空间上三次-四次混合型函数方程的Hyers-Ulam-Rassias稳定性

该文研究了2-Banach空间上三次-四次混合型函数方程f(kx+y)+f(kx-y)=(k^2+k)/2[f(x+y)+f(x-y)]+(k^2-k)/2[f(-x-y)+f(y-x)]+(k^4+k^3-k^2-k)f(x)+(k^4-k^3-k^2+k)f(-x)-(k^2-1)f(y)-(k^2-1)f(-y)的一般解和Hyers-Ulam-Rassias稳定性,这里k>1.该文的结果提升和推广了已有的相关结果.     

一类源自可加、二次、三次和四次映射的泛函方程的模糊稳定性

在模糊Banach空间中研究了混合泛函方程f(x+ky)+f(x-ky)=k~2f(x+y)+k~2f(x-y)+2(1-k~2)f(x)+(k~2(k~2-1))/12(f(2y)-4f(y))的Hyers-Ulam稳定性,这里k>1是固定的一个整数,f(y)=f(y)+f(-y).     

QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES

In this paper,we solve the quadratic p-functional inequalities‖f(x+y)+f(x-y)-2f(x)-2f(y)‖≤‖ρ(2f((x+y)/2)+2f((x-y)/2)-f(x)-f(y))‖,(0.1)where ρ is a fixed complex number with |ρ| 1,and‖2f((x+y)/2)+2f((x-y)/2)-f(x)-f(y)‖≤‖ρ(f(x+y)+f(x-y)-2f(x)-2f(y))‖,(0.2)where ρ is a fixed complex number with |ρ| 1/2.Using the direct method,we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities(0.1) and(0.2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with the quadratic ρ-functional inequalities(0.1)and(0.2) in complex Banach spaces.     

拟Banach空间上含参数的二次-可加混合型函数方程的解和Hyers-Ulam-Rassias稳定性

该文讨论了带有参数s的二次-可加混合型函数方程2k[f(x+ky)+f(kx+y)]=k(1-s+k+ks+2k~2)f(x+y)+k(1-s-3k+ks+2k~2)f(x-y)+2kf(kx)+2k(s+k-ks-2k~2)f(x)+2(1-k-s)f(ky)+2ksf(y)的一般解,同时研究了该函数方程在拟Banach空间上的Hyers-Ulam-Rassias稳定性,这里k1,s≠1-2k.     

一样的赋值与不一样的结果

已知函数f(x)对任意实数x、y都有f(x+y)=f(x)+2y(x+y),且f(1)=1,求f(x)的表达式.分析1因为对任意实数x、y都有     

特征为2的素环上强保持k-交换性的映射

令R是特征为2,且含有非平凡幂等元与单位元的素环.假设f:R→R是满射,k=2,3.证明了,f满足[f(x),f(y)]_k=[x,y]_k=[[x,y]_(k-1),y]对所有元x,y∈R成立当且仅当存在映射μ:R→C和元λ∈C使得f(x)=λx+μ(x)对所有元x∈R成立,其中λ~(k+1)=1,C是R的扩展中心.     

矩阵拟范空间上函数方程的Ulam稳定性

本文给出了矩阵拟范空间的定义,并在其上讨论了混合二次一三次函数方程6f(x+y)-6f(x-y)+4f(3y)=3f(x+2y)-3f(x-2y)+9f(2y)的Ulam稳定性.     

On the stability of a mixed functional equation deriving from additive,quadratic and cubic mappings

In this paper, we investigate the general solution and the Hyers–Ulam stability of the following mixed functional equation f(2x + y) + f(2x- y) = 2f(2x) + 2f(x + y) + 2f(x- y)- 4f(x)- f(y)- f(-y)deriving from additive, quadratic and cubic mappings on Banach spaces.     

一个问题的分析与拓展

题:已知f(x)是定义在[0,1]上的非负函数,且f(1)=1,对任意x,y,x+y∈[0,1]都有:f(x+y)≥f(x)+f(y),求证:f(x)≤2x(x∈[0,1]).本题为2011年清华大学保送生考试题,难度     

On I-Covering Mappings and 1-I-Covering Mappings

In this paper, we introduce the concepts of I-covering mappings and 1-I-covering mappings, discuss the difference between sequence-covering and I-covering mappings by some examples. With those concepts, we get some interesting properties of I-covering(1-I-covering)mappings and some characterizations of I-covering(1-I-covering) and compact mapping images of metric spaces.     

Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings

In this paper, we introduce an iteration process of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for an inverse strongly-monotone mapping, and then obtain a weak convergence theorem. Using this result, we obtain a weak convergence theorem for a pair of a nonexpansive mapping and a strictly pseudocontractive mapping. Further, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping.     

(λ,μ]-模糊映射与HX-模糊映射

通过引入((β),(α),)-模糊映射的定义,给出了(α,β)-模糊映射的另外四种形式,并将(∈,∈)-模糊映射、(∈,∈∨(q))-模糊映射和(∈,∈,∨,q)-模糊映射推广成具有边界值的(λ,μ]-模糊映射. 讨论了(λ,μ]-模糊映射与HX-模糊映射的关系. 使人们更加清楚地认识到了HX-模糊映射的意义.     

关于非扩张映射和单调映射的一般迭代方法

该文的目的是通过研究一个一般的迭代过程, 来寻求一族非扩张映射的不动点集与强单调映射的变差不等式解集的公共元素.     

单叶调和映射

由于在极小曲面理论中的作用，对调和映射的研究已有较长时间。１９８４年以来，经典解析单叶映射的理论被推广至调和单叶映射，并获得许多结论。这些工作引起人们对它的浓厚兴趣。该文介绍这一课题某些重要成果的概貌，并指出一些尚未解决的问题。它共分六个部分：映射定理；单叶调和函数的数值估计；特殊映射；变分方法；境界性质和在极小曲面中的应用。     

On Projective Mappings

Mathematical Notes - Let X,Y be Polish spaces, and let $\mathcal{B}_k $ be the σ-algebra generated by the projective class $L_{2k + 1} $ . A mapping $f:X \mapsto Y$ is called $k$...     

Bounded-Norm Matrix-Inverse Mappings

This paper introduces the concept of bounded-norm matrix-inversemappings, i.e. mappings µ : R^mxnR^nxm such that, for allnonzero mxn matrices A, the matrix µ(A) is a generalizedinverse of A and ||µ(A)||> k/s(A), where K < 0 isa constant and s(A) is the nonzero singular value of A havingsmallest absolute value. It is shown how the definition of suchmappings is motivated by the need to ensure finite terminationof the inner-iterations of generalized elimination methods forthe solution of nonlinearly constrained optimization problems.The main result of the paper is that the mapping defined byµ(A) = A^b is a bounded-norm matrix-inverse mapping, providedthat the basic inverse A^b is calculated using Gaussian eliminationwith complete pivoting. The concept of bounded-norm matrix-inversemappings is then extended to that of boundednorm least-squaresmatrix-inverse mappings. It is proved that the mapping definedby µ(A) = A^ß is a bounded-norm least-squaresmatrix-inverse mapping, provided that the basic least-squaresinverse A^ß is calculated using the QR decompositionwith column pivoting.     

调和典则实映照

本文从几何函数论的观点研究了一类复值调和典则实函数，在某些假定之下形成了类Ｔ＿Ｈ和它的子类Ｔ￣０＿Ｈ，并给出了Ｔ＿Ｈ和Ｔ￣０＿Ｈ的闭凸壳ＨＴ＿Ｈ和ＨＴ￣０＿Ｈ文中证明了Ｔ＿Ｈ是正规的，Ｔ￣０＿Ｈ是紧的。Ｔ￣０＿Ｈ与ＨＴ￣０＿Ｈ中的函数可用积分公式表示。