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1. Let X be the conjugate of a separable Banach space satifying the *-Opial condition, i. e., if $\{ {x_n}\} \subset x,{x_n}\mathop \to \limits^{{w^*}} {x_\infty },{x_\infty } \ne y$, then$\mathop {\overline {\lim } }\limits_{n \to \infty } ||{x_n} - {x_\infty }|| < \mathop {\overline {\lim } }\limits_{n \to \infty } ||{x_n} - y||$ for rxample $X = {l_1}$ Let K be a nonempty weak* closed convex subset of X. The main results are: Theorem 1. Suppose T is a ooniinuons mappings of K into itself such that for every $x,y \in K$，$||Tx - Ty|| \le a||x - y|| + b\{ ||x - Tx|| + ||y - Ty||\} + c\{ ||x - Ty|| + ||y - Tx||\}$ where real numbers $a,b,c \ge 0$ and $a + 2b + 2c = 1$. Suppose also K is bounded.Then T has at least one fixed point in K. Theorem 2. Let T be a mapping of K into itself, and $a(x,y),b(x,y),c(x,y)$be real functions such that for all$x,y \in K$ $||Tx - Ty|| \le a(x,y)||x - y|| + b(x,y)\{ ||x - Tx|| + ||y - Ty||\} + c(x,y)\{ ||x - Ty|| + ||y - Tx||\}$ and $a(x{\rm{y}},y){\rm{ + }}2b(x,y){\rm{ + }}2c(x,y) \le 1$ Suppose there exists $x \in K$ such that $O(x) = \{ {T^n}x\} _{n = 1}^\infty$ is bounded and $\mathop {\inf }\limits_{y,z \in o(x)} c(y,z) > 0$ Then T has at least one fixed point z in K and ${T^n}x\mathop \to \limits^{{w^*}} z$. 2. We denote $CL(x) = \{ A;nonempty{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} closed{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} subset{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} of{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} X\}$ $K(x) = A;nonempty{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} closed{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} subset{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} of{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} x\}$ here X is a complete metric space with metric d. On $CL(x)$ and $K(x)$ we introduce the generalized Hausdorff distance $H(,)$, The main results are: Theorem 3. Suppose $\{ T,S\}$ is a pair of set-valued mappings of X into $CL(x)$,which satisfies the following condition: $H(Tx,Sy) \le hMax\{ d(x,y),D(x,Tx),D(y,Sy),\frac{1}{2}[D(x,Sy) + D(y,Tx)]\}$ for each $x,y \in K$, where 0相似文献

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Let X be a complete metric space with, distance fcmction d, and T a mapping from X into X. T is said to be a contractive mapping (25), if it satisfies tbe following condition d(Tx, Ty) 相似文献

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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.  相似文献

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The main result of this paper states as follows: Assume that for a closed ball D @ 0 and with center at the origin, a mapping T : D M D satisfies $$T(0) = 0\ \hbox{and}\ \vert \langle Tx, Ty \rangle - \langle x, y \rangle \vert \leq \varepsilon \eqno (1)$$ for some 0 h l < min { 1/4, d 2 /17} and for all x , y ] D . Then, there exists an isometry I : D M D with  \vert Tx - Ix \vert \le \left\{ {\matrix{ {13\sqrt \varepsilon } \hfill &{{\rm for}\; d  相似文献

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A collection F of operators on a vector space V is said to be semitransitive if for every pair of nonzero vectors x and y in V there exists a member T of F such that either Tx = y or Ty = x (or both). We study semitransitive algebras and semigroups of operators. One of the main results is that if the underlying field is algebraically closed, then every semitransitive algebra of operators on a space of dimension n contains a nilpotent element of index n. Among other results on semitransitive semigroups, we show that if the rank of nonzero members of such a semigroup acting on an n-dimensional space is a constant k, then k divides n.  相似文献

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In this paper, we give the answer to the following problem: Let (Xd) be a complete metric space and let T be a mapping on X satisfying $$d(Tx, Ty) < d(x, y)$$ for any $$x, y \in X$$ with $$x \ne y$$. Then what are the weakest additional assumptions to imply the same conclusion as in the Banach contraction principle?  相似文献

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<正> §1.引言 凡合條件即是說凡合條件kk[x,y]=kk[x,y](1.1)的核k(x,y)叫做正規核(normal kernel).這種核顯然包括實對稱核、實畸對稱核、艾氏核及畸艾氏核等為特例。在本文中,我們將討論具此種核之積分方程之性質及解法尤其是關於此種核之特值及奇值(即希米特(E.Schmidt)的特值)之性質  相似文献

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Banach空间中的平均非扩张映象:不动点的存在定理   总被引：7，自引：0，他引：7

<正> 设X是Banach空间,E是X中的集合,T是映集合E到自身的映象.若T满足条件(称为平均非扩张条件)其中x,y∈E,a,b,c≥0且a+2b+2c≤1,则称T是平均非扩张映象. 文[1]概括了近年来研究关于平均非扩张映象不动点的一些主要结果.本文进  相似文献

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61. IntroductionLet (M, g) be a compact smooth foemannian manifOld of dimension n with C2 boundary0M, and (N, h) be a smooth compact Riemannian manifolds of dimension k. Assume that(N, h) without boundary is isometrically embedded into the Euclidean space (Rm, (., .)).We assume that Sobolev spaceHl (M, N) = {u E Hl (M; R',.)lu(x) E N for a.e.x E M}and for every u E H1 (M; N), define the energy of u,E(u) = / lVuI'dv, (1.1)j. lVuI'dv, (1.1)where in local coordinate 1VuI' = g"pff 3, …  相似文献

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