The question on multipliers in L 1 and C

The connection between Belinsky?CDveyrin?CMalamud??s theorem on multipliers and some other known theorems on multipliers in the spaces L ¹ and C is clarified. It is shown that Belinsky?CDveyrin?CMalamud??s theorem can be obtained from them. The relevant examples of multipliers in the spaces L ¹ and C indicating the nonequivalence of the compared theorems are presented.     

On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems

In this paper, the author first introduces the concept of generalized algebraic cone metric spaces and some elementary results concerning generalized algebraic cone metric spaces. Next, by using these results, some new fixed point theorems on generalized (complete) algebraic cone metric spaces are proved and an example is given. As a consequence, the main results generalize the corresponding results in complete algebraic cone metric spaces and generalized complete metric spaces.     

Fixed and periodic point results in cone metric spaces

Huang and Zhang [L.-G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476] proved some fixed point theorems in cone metric spaces. In this work we prove some fixed point theorems in cone metric spaces, including results which generalize those from Haung and Zhang’s work. Given the fact that, in a cone, one has only a partial ordering, it is doubtful that their Theorem 2.1 can be further generalized. We also show that these maps have no nontrivial periodic points.     

乘积G-凸空间内的非空交定理和广义矢量平衡问题组

利用作者在G-凸空间内对集值映象簇得到的一个极大元存在性定理,在非紧乘积G-空间内,对集值映象簇建立了某些新的非空交定理．作为应用, 在非紧乘积G-凸空间内, 对广义矢量平衡问题组证明了一些平衡存在性定理．这些定理统一、改进和推广了文献中一些重要的已知结果．     

Martingales and some integrability criterions for multiple trigonometric series

Applying some martingale properties of the sequences of cubic partial sums of series in the Haar multiple system, some integrability criterions for multiple trigonometric series are established. Some of the proved theorems improve and extend to the multiple trigonometric series the classical theorems on integrability of one-dimensional trigonometric series, the proofs of which are based on Helly??s principal of choice.     

超凸空间中的连续选择定理与耦合定理

本文给出了超凸空间中的连续选择定理与耦合定理，并得到了它们的证明,作为应用，我们给出了超凸空间中的不动点定理与截口定理．     

关于Banach空间中Lipschitz映象对的公共不动点的存在性

证明了p一致凸Banach空间中Lipschitz映象对的公共不动点的存在性。利用这个结果,在Hilbert空间,Lp空间,Hardy空间Hp,Sobolev空间Hr,p,1<p<∞,r≥0,也建立了这些映象的若干公共不动点定理。     

局部FC-一致空间内具有联立广义矢量拟平衡组约束的数学规划(英文)

在局部FC-一致空间内引入和研究了某些新的联立广义矢量拟平衡问题组和具有联立广义矢量拟平衡组约束的数学规划.应用作者在局部FC-一致空间得到的Himmelberg型不动点定理,首先在局部FC-一致空间内对联立广义矢量拟平衡问题组的解证明了某些新的存在性定理.作为应用,对具有联立广义矢量拟平衡组约束的数学规划的解得到了某些新的存在性定理.     

局部凸空间中的不动点定理及其应用

讨论了局部凸空间中推广的Leray-Schauder度的基本性质,建立了一些新的不动点定理,并给出了对局部凸空间Cauchy初值问题的应用.这些定理是Banach空间中相应结果的推广.     

Strong convergence theorems for strictly asymptotically pseudocontractive mappings in Hilbert spaces

The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a Hilbert space. Under suitable conditions some strong convergence theorems are proved. The results presented in the paper are new which extend and improve some recent results of Acedo and Xu [Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 67(7), 2258??271 (2007)], Kim and Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140??152 (2006)], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400??411 (2006)], Nakajo and Takahashi [Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. Math. Anal. Appl., 279, 372??79 (2003)], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329(1), 336??46 (2007)], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334??345 (2007)], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26(11), 1835??842 (1996)], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12 (2), 77??8 (2002)], Gu [The new composite implicit iteration process with errors for common fixed points of a finite family of strictly pseudocontractive mappings. J. Math. Anal. Appl., 329, 766??76 (2007)].     

Dilations of Some VH-Spaces Operator Valued Invariant Kernels

We investigate VH-spaces (Vector Hilbert spaces, or Loynes spaces) operator valued Hermitian kernels that are invariant under actions of *-semigroups from the point of view of generation of *-representations, linearizations (Kolmogorov decompositions), and reproducing kernel spaces. We obtain a general dilation theorem in both Kolmogorov and reproducing kernel space representations, that unifies many dilation results, in particular B. Sz.-Nagy??s and Stinesprings?? dilation type theorems.     

弱拓扑下的非线性随机积分和微分方程组的解*

在本文中,我们首先对具有随机定义域的弱连续随机算子组证明了一个Darbo型随机不动点定理.利用这一定理,我们对Banach空间中关于弱拓扑的非线性随机Volterra积分方程组给出了随机解的存在性准则.作为应用,我们得到了非线性随机微分方程组的Canchy问题弱随机解的存在定理.也得到了这些随机方程组在Banach空间中关于弱拓扑的极值随机解的存在性和随机比较结果.我们的定理改进和推广了Szep,Mitchell－Smith,Cramer－Lakshmikantham,Lakshmikantham-Leela和丁的相应结果.     

Generalized Motzkin Theorems of the Alternative and Vector Optimization Problems

In this paper, we introduce a definition of generalized convexlike functions (preconvexlike functions). Then, under the weakened convexity, we study vector optimization problems in Hausdorff topological linear spaces. We establish some generalized Motzkin theorems of the alternative. By use of these theorems of the alternative, we obtain some Lagrangian multiplier theorems. A saddle-point theorem and a scalarization theorem are also derived.Communicated by F. GiannessiThe author thank Ginndomenico Mastrocni for helpful and useful comments.     

KKM TYPE THEOREMS AND COINCIDENCE THEOREMS ON L-CONVEX SPACES

Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex spaces. As applications, some new fixed point theorems are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature.     

WEAK ATOMIC DECOMPOSITIONS OF MARTINGALE HARDY-LORENTZ SPACES AND APPLICATIONS＊

In this article,we establish some atomic decomposition theorems for martingale Hardy-Lorentz spaces.As applications,with the help of weak atomic decompositions,some interpolation theorems for martingal...     

没有紧性, 连续性和凹性的多准则对策的帕雷多平衡*

在本文中利用作者得到的一极小极大不等式,对不具有紧性,连续性和四性的多准则对策在拓扑矢量空间和自反Banach空间内证明了某些帕雷多平衡存在定理。     

Collectively fixed-point theorems in noncompact G-convex spaces

In this paper, by applying the technique of continuous partition of unity and Tychonoff's fixed-point theorem, some new collectively fixed-point theorems for a family of set-valued mappings defined on the product space of noncompact G-convex spaces are proved. Our theorems improve, unify, and generalize many important collectively fixed-point theorems in recent literature.     

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

In this paper we first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multi-valued mappings on metric spaces. Our main results improve and extend several known results proved by other authors.     

Equivalent moduli of continuity, Bloch’s theorem for pluriharmonic mappings in \mathbb{B}{\kern-8pt}\mathbb{B}^{\boldsymbol n}

In this paper, we first establish a Schwarz?CPick type theorem for pluriharmonic mappings and then we apply it to discuss the equivalent norms on Lipschitz-type spaces. Finally, we obtain several Landau??s and Bloch??s type theorems for pluriharmonic mappings.     

乘积拓扑矢量空间中的不动点定理和广义矢量平衡问题组

利用零调映象的一个不动点定理,在乘积拓扑矢量空间内得到了某些新的不动点定理,作为应用,在乘积拓扑矢量空间内,对一类广义矢量平衡问题组证明了一些平衡存在性定理,这些定理推广了近期文献中的一些重要的已知结果.