Ishikawa iterative process with errors for nonlinear equations of generalized monotone type in Banach spaces

The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let X be a real Banach space and T : D ? X → 2^D be a multi‐valued operator of generalized monotone type with fixed points. A new general lemma on the convergence of real sequences is proved and used to show that {xn} converges strongly to a unique fixed point of T in D. This result is applied to the iterative approximation method for solutions of nonlinear equations with generalized strongly accretive operators. Our results generalize many of know results. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rolle定理的逆证新思考

Rolle定理是微分中值定理中最基本、最重要的,其证明具有广泛的代表性.本文侧重从分析定理的条件着手,利用反证法并借助确界原理、闭区间套原理等不同理论,给出了Rolle定理一些新的证法.     

Tailoring the liquid crystalline property via controlling the generation of dendronized polymers containing azobenzene mesogen

The first‐ and second‐generation dendronized polymers containing azobenzene mesogen were designed and successfully synthesized via free radical polymerization. The chemical structures of the monomers were confirmed by elemental analysis, ¹H NMR, and ¹³C NMR. The molecular characterizations of the polymers were performed with ¹H NMR and gel permeation chromatography. The phase structures and transition behaviors were studied using differential scanning calorimetry, polarized light microscopy, and small‐angle X‐ray scatter experiments. The experiment results revealed that the first‐generation dendronized polymer exhibited liquid crystalline behavior of the conventional side‐chain liquid crystalline polymer with azobenzene mesogen, that is, the polymer exhibited smectic phase structure at lower temperature and nematic phase structure at higher temperature. However, the second‐generation dendronized polymers exhibited more versatile intriguing liquid crystalline structures, namely smectic phase structure at lower temperature and columnar nematic phase structure at higher temperature, and moreover, the phase structure still remained before the decomposition temperature. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1149–1159, 2010     

Banach空间中完全广义混合隐似平衡问题的辅助原理和迭代算法

在Banach空间中利用双线性连续泛函F代替内积引进了新的一类完全广义混合隐似平衡问题，引进了F强单调的概念，提出了该平衡问题的广义辅助问题，证明了广义辅助问题的收敛定理，给出了新的算法和由此算法产生的迭代序列的收敛特征．     

双退化拟线性椭圆型方程Keldys-Fichera障碍问题

讨论一类双退化散度型拟线性椭圆型方程的Keldys-Fichera障碍问题,证明了解的存在性.     

Photoresponsive poly(methyl methacrylate)‐b‐azodendron block copolymers prepared by ATRP and click chemistry

A range of block copolymers (BCs) consisting of a linear poly(methyl methacrylate) (PMMA) block linked to an aliphatic polyester dendron functionalized with azobenzene moieties have been synthesized by sequential atom transfer radical polymerization (ATRP) and Click Chemistry. Two alkyne‐functionalized PMMA homopolymers with different molecular weights were obtained by ATRP and coupled to generations 2 to 4 of azodendrons bearing an azide group at the focal points. In the case of the azodendron with the highest generation number, the length of the flexible spacer attaching the cyanoazobenzene units to the dendron has also been modified. The coupling of both blocks and purity of BCs were checked by gel permeation chromatography, nuclear magnetic resonance, and infrared spectroscopy. The thermal transitions and liquid crystalline behavior of the BCs were investigated by differential scanning calorimetry and polarized‐light optical microscopy. A morphological study was carried out by transmission electron microscopy, using samples annealed at 115 °C. Photo‐induced anisotropy was induced in thin films of these materials after annealed at 115 °C. The highest stable birefringence values were obtained for the BCs bearing 8 and 16 azobenzene units in the dendritic block. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1538–1550, 2010     

Parametric Proximal-Point Methods

The main purpose of the present work is to introduce two parametric proximal-point type algorithms involving the gradient (or subdifferential) of a convex function. We take advantage of some properties of maximal monotone operators to prove monotonicity and convergence rate conditions. One example in Hilbert spaces and two numerical examples with program realizations are presented.     

Maximality of sums of two maximal monotone operators in general Banach space

We combine methods from convex analysis, based on a function of Simon Fitzpatrick, with a fine recent idea due to Voisei, to prove maximality of the sum of two maximal monotone operators in Banach space under various natural domain and transversality conditions.

     

Extremal Solutions and Strong Relaxation for Second Order Multivalued Boundary Value Problems

In this paper we study semilinear second order differential inclusions involving a multivalued maximal monotone operator. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain “extremal” solutions and we prove a strong relaxation theorem. This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants No. 2 P03A 003 25 and No. 4 T07A 027 26.     

与p-Laplace算子相关的Neumann边值问题解的存在性

利用Calvert和Gupta关于非线性增生映射值域的扰动理论,研究了与p-Laplace算子相关的非线性边值问题在L~s(Ω)空间中解的存在性,其中(2N/N 1)＜p(?)s＜ ∞且N(?)1．文中采用了一些新的证明技巧,推广和补充了笔者以往的研究工作．