共查询到20条相似文献,搜索用时 0 毫秒
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Reza Saadati S. Mansour Vaezpour 《Journal of Mathematical Analysis and Applications》2008,346(2):446-450
In this paper, we consider strongly bounded linear operators on a finite dimensional probabilistic normed space and define the topological isomorphism between probabilistic normed spaces. Then we prove that every finite dimensional probabilistic normed space which is a topological vector space is complete. 相似文献
3.
William J. Rolli 《Journal of Mathematical Analysis and Applications》2006,321(1):388-395
In this paper, we use the characterization of frames, introduced in [W. Rolli, A characterization of frames for finite dimensional Hilbert spaces, preprint], to construct frames for finite dimensional Hilbert spaces. Furthermore this approach allows for the construction of frames with prescribed properties. 相似文献
4.
Chun-Gil Park 《Proceedings of the American Mathematical Society》2003,131(8):2501-2504
We prove the stability of multi-quadratic functional equations in Banach spaces.
5.
The subject of this paper is the systematic study of second order notions concerning differentiable functions with Lipschitz
derivative. The results and notions are motivated by recent papers of Cominetti, Correa and Hiriart-Urruty. The first goal
of this paper is the comparison of several known second order directional derivatives. The second goal is the introduction
of a generalized Hessian which is a set of certain symmetric bilinear forms. The relation of this generalized Hessian to other
existing second order derivatives is also described.
The research was supported by a grant from the National Science Foundation NSF-66-2270, which is gratefully acknowledged.
Research supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T-016846 and by the Humboldt
Foundation. 相似文献
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Shih-Sen Chang 《Journal of Mathematical Analysis and Applications》2006,323(2):1402-1416
By using viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for the iterative sequence to converging to a common fixed point are obtained. The results presented in the paper extend and improve some recent results in [H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279-291; H.K. Xu, Remark on an iterative method for nonexpansive mappings, Comm. Appl. Nonlinear Anal. 10 (2003) 67-75; H.H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 202 (1996) 150-159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957-961; J.S. Jung, Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 302 (2005) 509-520; P.L. Lions, Approximation de points fixes de contractions', C. R. Acad. Sci. Paris Sér. A 284 (1977) 1357-1359; A. Moudafi, Viscosity approximation methods for fixed point problems, J. Math. Anal. Appl. 241 (2000) 46-55; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 128-292; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491]. 相似文献
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In this paper we consider two classes of equilibrium problems which imply general α-pseudomonotonicity and general α-semipseudomonotonicity relative to a set-valued map on reflexive and nonreflexive Banach spaces, respectively. Using the classical KKM technique, we obtain some existence results under boundedness as well as under unboundedness assumptions. Some examples are given. 相似文献
10.
In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent
and we study the notion ofD-compactness and D-boundedness in probabilistic normed spaces. 相似文献
11.
Huang Jianfeng Wang Yuanheng 《高校应用数学学报(英文版)》2007,22(3):311-315
This paper studies the convergence of the sequence defined by x0∈C,xn 1=αnu (1-αn)Txn,n=0,1,2,…, where 0 ≤αn ≤ 1, limn→∞αn = 0, ∑∞n=0 αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results. 相似文献
12.
《Mathematische Nachrichten》2017,290(17-18):2788-2799
A well‐known result of J. Lindenstrauss and A. Pełczyński (1968) gives the existence of a universal non‐weakly compact operator between Banach spaces. We show the existence of universal non‐Rosenthal, non‐limited, and non‐Grothendieck operators. We also prove that there does not exist a universal non‐Dunford–Pettis operator, but there is a universal class of non‐Dunford–Pettis operators. Moreover, we show that, for several classes of polynomials between Banach spaces, including the non‐weakly compact polynomials, there does not exist a universal polynomial. 相似文献
13.
S. Hu and Y. Sun [S. Hu, Y. Sun, Fixed point index for weakly inward mappings, J. Math. Anal. Appl. 172 (1993) 266-273] defined the fixed point index for weakly inward mappings, investigated its properties and studied the fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we continue to investigate boundary conditions, under which the fixed point index for the completely continuous and weakly inward mapping, denoted by i(A,Ω,P), is equal to 1 or 0. Correspondingly, we can obtain some new fixed point theorems of the completely continuous and weakly inward mappings and existence theorems of solutions for the equations Ax=μx, which extend many famous theorems such as Leray-Schauder's theorem, Rothe's two theorems, Krasnoselskii's theorem, Altman's theorem, Petryshyn's theorem, etc., to the case of weakly inward mappings. In addition, our conclusions and methods are different from the ones in many recent works. 相似文献
14.
Marija S. ?iri? Milan Lj. Zlatanovi? Mi?a S. Stankovi? Ljubica S. Velimirovi? 《Applied mathematics and computation》2012,218(12):6648-6655
In this paper geodesic mappings of equidistant generalized Riemannian spaces are discussed. It is proved that each equidistant generalized Riemannian space of basic type admits non-trivial geodesic mapping with preserved equidistant congruence. Especially, there exists non-trivial geodesic mapping of equidistant generalized Riemannian space onto equidistant Riemannian space. An example of geodesic mapping of an equidistant generalized Riemannian spaces is presented. 相似文献
15.
Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces 总被引:1,自引:0,他引:1
In this paper, we modify Halpern and Mann’s iterations for finding a fixed point of a relatively nonexpansive mapping in a Banach space. Consequently, a strong convergence theorem for a nonspreading mapping is deduced. Using a concept of duality theorems, we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings. Finally, we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space. 相似文献
16.
Abdul Rahim Khan Abdul-Aziz Domlo 《Journal of Mathematical Analysis and Applications》2008,341(1):1-11
In this paper, we introduce a general iteration scheme for a finite family of asymptotically quasi-nonexpansive mappings. The new iterative scheme includes the modified Mann and Ishikawa iterations, three-step iterative scheme of Xu and Noor and Khan and Takahashi scheme as special cases. Our results are generalizations as well as refinement of several known results in the current literature. 相似文献
17.
H. G. Eggleston 《Israel Journal of Mathematics》1965,3(3):163-172
In Euclidean space a set of constant width has the property that it is not a proper subset of any set of the same diameter.
The converse implication is also true. Here we show that if Euclidean is replaced byn-dimensional Banach space the direct statement is true, but the converse statement is false. Attention is drawn to the problem
of characterising those Banach spaces of finite dimension for which the converse is true. 相似文献
18.
Taizo Kanenobu 《Topology and its Applications》1985,19(2):123-127
As an analogue of the classical cable knot, the p-cable n-knot about an n-knot K, where p is an integer and n?2, is defined, and some basic properties of higher dimensional cable knots are described. We show that for p>0 then p-fold branched cyclic covering space of an (n+2)-sphere branched over the p-cable knot about an n-knot K is an (n+2)-sphere or a homotopy (n+2)-sphere which is the result of Gluck-surgery on the composition of p copies of K according as if p is odd or even. At the same time, we prove that for any n?2 and p?2, the composition of p copies of any n-knot K is the fixed point set of a Zp-action on an (n+2)-sphere. This is another counterexample to the higher dimensional Smith conjecture. 相似文献
19.
Viscosity approximation methods for a family of finite nonexpansive mappings are established in Banach spaces. The main theorems extend the main results of Moudafi [Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl. 241 (2000) 46–55] and Xu [Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279–291] to the case of finite mappings. Our results also improve and unify the corresponding results of Bauschke [The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996) 150–159], Browder [Convergence of approximations to fixed points of nonexpansive mappings in Banach spaces, Archiv. Ration. Mech. Anal. 24 (1967) 82–90], Cho et al. [Some control conditions on iterative methods, Commun. Appl. Nonlinear Anal. 12 (2) (2005) 27–34], Ha and Jung [Strong convergence theorems for accretive operators in Banach spaces, J. Math. Anal. Appl. 147 (1990) 330–339], Halpern [Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957–961], Jung [Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 302 (2005) 509–520], Jung et al. [Iterative schemes with some control conditions for a family of finite nonexpansive mappings in Banach space, Fixed Point Theory Appl. 2005 (2) (2005) 125–135], Jung and Kim [Convergence of approximate sequences for compositions of nonexpansive mappings in Banach spaces, Bull. Korean Math. Soc. 34 (1) (1997) 93–102], Lions [Approximation de points fixes de contractions, C.R. Acad. Sci. Ser. A-B, Paris 284 (1977) 1357–1359], O’Hara et al. [Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces, Nonlinear Anal. 54 (2003) 1417–1426], Reich [Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 287–292], Shioji and Takahashi [Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces, Proc. Amer. Math. Soc. 125 (12) (1997) 3641–3645], Takahashi and Ueda [On Reich's strong convergence theorems for resolvents of accretive operators, J. Math. Anal. Appl. 104 (1984) 546–553], Wittmann [Approximation of fixed points of nonexpansive mappings, Arch. Math. 59 (1992) 486–491], Xu [Iterative algorithms for nonlinear operators, J. London Math. Soc. 66 (2) (2002) 240–256], and Zhou et al. [Strong convergence theorems on an iterative method for a family nonexpansive mappings in reflexive Banach spaces, Appl. Math. Comput., in press] among others. 相似文献
20.
Suppose thatX andY are real Banach spaces,U ⊂X is an open bounded set star-shaped with respect to some point,n, k ∈ ℕ,k <n, andMn, k (U,Y) is the sharp constant in the Markov type inequality for derivatives of polynomial mappings. It is proved that for anyM ≥M
n,k
(U, Y) there exists a constantB > 0 such that for any functionf ∈C
n
(U, Y) the following inequality holds:
The constantM =M
n−1,k
(U, Y) is best possible in the sense thatM
n−1,k
(U, Y) = infM, where inf is taken over allM such that for someB > 0 the estimate holds for allf ∈C
n
(U, Y).
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 332–342, March, 1998.
This research was partially supported by the International Science Foundation under grant No. U92000. and by the State Committee
of the Ukraine for Science and Technology. 相似文献