Fixed point theorems in symmetric spaces and applications to probabilistic spaces

Several fixed point theorems for symmetric spaces are proved. Then these theorems are used in symmetric PPM-space to prove and generalize Theorem 6 of [T.L. Hicks, B.E. Rhoades, Fixed point theory in symmetric spaces with applications to probabilistic spaces, Nonlinear Anal. 36 (1999) 331-344].     

The Bochner technique and modification of the Ricci tensor

In the well-known vanishing theorems of Bochner, the assumptions Ric ≥ 0 and Ric ≤ 0 are modified by using Hessian and Laplacian of a smooth positive function such that, when this function is constant, these assumptions return to Ric ≥ 0 and Ric ≤ 0. We prove that the assertions and results of Bochner’s vanishing theorems still hold under these modified assumptions. Additionally, the assumption Ric ≥ H > 0 given in the eigenvalue estimate theorem of Lichnerowicz is also modified in the same way, and we obtain estimates for the first positive eigenvalue of the Laplace operator.     

Sperner’s lemma and zero point theorems on a discrete simplex and a discrete simplotope

We show two discrete zero point theorems that are derived from Sperner’s lemma and a Sperner-like theorem (van der Laan and Talman [Math. Oper. Res. (1982)] [5]; Freund [Math. Oper. Res. (1986)]) [3]. Applications to economic and game models are also presented.     

一般Lidstone边值问题的解的存在性

考察了含有各阶导数的一般Lidstone边值问题的存在性. 利用Leray-Schauder不动点定理、等价范数及积分方程组技巧证明了解或正解的两个存在定理. 这些定理在应用上非常方便. 换句话说, 通过考察非线性项在某个有界子集上的“高度”就能决定解的存在性.     

Approximations for nonlinear mappings by the hybrid method in Hilbert spaces

The hybrid method in mathematical programming was introduced by Haugazeau (1968) [1] and he proved a strong convergence theorem for finding a common element of finite nonempty closed convex subsets of a real Hilbert space. Later, Bauschke and Combettes (2001) [2] proposed some condition for a family of mappings (the so-called coherent condition) and established interesting results by the hybrid method. The authors (Nakajo et al., 2009) [10] extended Bauschke and Combettes’s results. In this paper, we introduce a condition weaker than the coherent condition and prove strong convergence theorems which generalize the results of Nakajo et al. (2009) [10]. And we get strong convergence theorems for a family of asymptotically κ-strict pseudo-contractions, a family of Lipschitz and pseudo-contractive mappings and a one-parameter uniformly Lipschitz semigroup of pseudo-contractive mappings.     

Existence Results for General Inclusions Using Generalized KKM Theorems with Applications to Minimax Problems

Applying generalized KKM-type theorems established in our previous paper (Khanh et al. in Nonlinear Anal. 71:1227–1234, 2009), we prove the existence of solutions to a general variational inclusion problem, which contains most of the existing results of this type. As applications, we obtain minimax theorems in various settings and saddle-point theorems in particular. Examples are given to explain advantages of our results.     

Pointwise convergence of Fourier-Jacobi series

The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesàro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C,δ) means for −1<δ≤α+1/2 is obtained. With the aid of the generalized translation in terms of Jacobi polynomials, pointwise convergence theorems of the (C,δ) means for δ>α+1/2 and equiconvergence theorems for −1<δ≤α+1/2 are proved. The analogues of the Lebesgue, Salem and Young theorems of the Cesàro means at the critical index δ=α+1/2 are established. Supported by the Natural Science Foundation of Beijing     

Von Neumann–Davis type theorems for HLPK and Sherman functionals on Eaton triples

Periodica Mathematica Hungarica - In this work, we generalize the von&nbsp;Neumann and Davis theorems on the extension of the convexity of a group-invariant norm (resp.&nbsp;function) from...     

Lagrange duality in canonical DC programming

We study Lagrange duality theorems for canonical DC programming problems. We show two types Lagrange duality results by using a decomposition method to infinite convex programming problems and by using a previous result by Lemaire (1998)  [6]. Also we observe these constraint qualifications for the duality theorems.     

Ergodic theorems for hybrid sequences in a Hilbert space with applications

In this paper, we introduce the notion of generalized hybrid sequences, extending the notion of nonexpansive sequences introduced and studied in our previous work Djafari Rouhani (1981, 1990, 1990, 1997, 2002, 2004, 2002)  , , , , ,  and , and prove ergodic and convergence theorems for such sequences in a Hilbert space H$H$. Subsequently, we apply our results to prove new fixed point theorems for generalized hybrid mappings, first introduced in Kocourek et al. (2010)  [14], Takahashi and Takeuchi (2011)  [20], defined on arbitrary nonempty subsets of H$H$.     

两类统计收敛的表示定理

本文证明了Banach空间X中的序列Δ(Δ~m)-统计收敛表示,以及Banach空间X中的双序列(双序列双-Lacunary)统计收敛的表示.     

拓扑空间上不动点和具有上下界的变分不等式

ωω根据广义凸空间上的KKM型定理和Fan-Browder型不动点定理, 得到了没有凸和线性结构且没有紧致框架的拓扑空间上的Φ -映射和弱Φ -映射的若干个新的不动点定理. 作为应用, 在非紧致的拓扑空间上讨论了具有上下界的变分不等式解的存在性问题.     

Point splitting and condorcet criteria

Summary and Conclusions  First impressions are not always right, especially in this field mostly inhabited by impossibility theorems. The actual properties of the voting procedure constructed violate the intuition that motivated the rule. The Rolling Stones’s sentence with which this paper started is quite apposite to Public Choice, where getting “what you want” is usually more difficult than it seems.     

非交换Hp空间理论的若干进展——纪念李国平院士吴新谋教授诞辰100周年

该文分两部分综述非交换H_p 空间理论的研究背景、发展线路以及某些最新进展.第一部分介绍非交换Hardy 空间理论, 包括有限次对角代数的基本性质 (如唯一正规态开拓性质、分解性质、对数模性、不变子空间性质等),Szeg\"{o} 与Riesz 型分解定理和H¹-BMO 对偶定理等. 第二部分综述非交换 H_p鞅空间理论, 主要介绍各种非交换鞅不等式以及作者与合作者在非交换Hardy 鞅空间原子分解方面获得的最新结果. 该文还给出了非交换H_p空间理论有待解决的一些问题 和潜在的发展方向.     

Filter matrix based on interpolation wavelets for solving Fredholm integral equations

The interpolation wavelet is used to solve the Fredholm integral equation of the second kind in this study. Hence, by the extension of interpolation wavelets that [−1, 1] is divided to 2^N+1 (N ⩾  − 1) subinterval, we have polynomials with a degree less than M + 1 in each new interval. Therefore, by considering the two-scale relation the filter coefficients and filter matrix are used as the proof of theorems. The important point is interpolation wavelets lead to more sparse matrix when we try to solve integral equation by an approximate kernel decomposed to a lower and upper resolution. Using n-time, where (n ⩾ 2), two-scale relation in this method errors of approximate solution as O((2^−(N+1))ⁿ⁺¹). Also, the filter coefficient simplifies the proof of some theorems and the order of convergence is estimated by numerical errors.     

Henstock–Kurzweil–Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space

The aim of this paper is to describe Henstock–Kurzweil–Pettis (HKP) integrable compact valued multifunctions. Such characterizations are known in case of functions (see Di Piazza and Musia? (2006)  [16]). It is also known (see Di Piazza and Musia? (2010)  [19]) that each HKP-integrable compact valued multifunction can be represented as a sum of a Pettis integrable multifunction and of an HKP-integrable function. Invoking to that decomposition, we present a pure topological characterization of integrability. Having applied the above results, we obtain two convergence theorems, that generalize results known for HKP-integrable functions. We emphasize also the special role played in the theory by weakly sequentially complete Banach spaces and by spaces possessing the Schur property.     

Existence of solutions for elliptic equations with discontinuous nonlinearities strong resonance at infinity

In the present paper, our main purposes are to study nonlinear elliptic equations with strong resonance at infinity. Some existence theorems for nontrivial solutions are obtained by using some nonsmooth critical point theorems in [N. C. Kourogenis, N. S. Papageorgiou, Nonsmooth critical point theory and Nonlinear elliptic equations at resonance, J. Austral. Math Soc. (Ser. A) 69 (2000) 245–271]. The two of our theorems generalize Theorems 0.1 and 5.2 in [P. Bartolo, V. Benci, D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity, Nonlinear Anal. TMA 7 (1983) 981–1012] to nonsmooth cases. Another theorem is new even if for the smooth case.     

全纯函数的正规族

本文证明了两个正规族定理,分别改进了张国明、孙伟和庞学诚的一个结果和徐焱的一个结果.     

RN中一类拟线性椭圆方程组非负解的存在性和多重性

利用极小极大原理和Lj usternik-Schnirelmann畴数理论,研究了RN中一类拟线性椭圆方程组.当2≤p,q＜N时,α≥0,β≥0满足α+β+2＞max{p,q}和α+1/p*+β+1/q*≤1,通过建立解的个数与正连续函数V和W达到极小值集合的拓扑量之间的关系,得到拟线性方程组至少存在catMδ (M)个不同的非负解.