SOME RESULTS ON GENERALIZED EQUILIBRIUM PROBLEMS INVOLVING STRICTLY PSEUDOCONTRACTIVE MAPPINGS

In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.

ISHIKAWA ITERATIVE PROCEDURE FOR APPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS

It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper provide the new convergence criteria and novel convergence rate estimate for Ishikawa iterative sequence.

CONVERGENCE RATE ESTIMATE OF ISHIKAWA ITERATIVE SEQUENCE FOR STRICTLY PSEUDOCONTRACTIVE MAPPINGS

Itis shown that any fixed point of each Lipschitzian,strictly pseudocontractive map- ping T on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure.The argument in this paper provides a convergence rate estimate. Moreover the resultin this paper improves,generalizes and summarizes some important and el- egant recent results

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings

This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.

Convergence Theorems of φ-pseudo Contractive Type Mappings in Normed Linear Spaces

In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.

混合Bregman投影算法在Banach空间中分裂不动点问题的强收敛性

在p-一致凸且一致光滑的Banach空间中,利用Bregman投影,构造一新的混合投影迭代算法,逼近Bregman拟严格伪压缩映射不动点集和分裂可行性问题的公共解.目的是将2017年Chen J Z,Hu H Y和Ceng L C的研究结果中的迭代系数α_(n)须满足0<c≤a_(n)≤d<1证明对α_(n)≡1或α_(n)≡0时亦成立.所得的结果是对2017年Chen J Z,Hu H Y和Ceng L C相应结果的拓展和补充.

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.

Semistrictly Convex Fuzzy Mappings

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.

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）, 2258-2271 （2007）], Kim and Xu [Strong convergence of modified Mann iterations for asymptoti- cally nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140-1152 （2006）], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400-2411 （2006）], Nakajo and Takahashi pings and nonexpansive semigroups. J. Math [Strong convergence theorems for nonexpansive map- Anal. Appl., 279, 372-379 （2003）], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329（1）, 336-346 （2007）], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334-1345 （2007）], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26（11）, 1835-1842 （1996）], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12（2）, 77-88 （2002）], Gu [The new composite implicit iteration process strictly pseudocontractive mappings. J. Math with errors for common fixed points of a finite family of Anal. Appl., 329, 766-776 （2007）].

Strong convergence theorem for a generalized equilibrium problem and a k-strict pseudocontraction in Hilbert spaces

The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a k-strict pseudocontractive mapping in the Hilbert space. The presented results extend and improve the corresponding results reported in the lit-erature.

The Connectedness of the Proper Efficient Solution Sets of the Vector Optimization Problem for a Strict Cone-quasiconvex Mapping

In this paper,we study the connectedness of proper efficient solution sets of the vector optimization problem for a strict cone--quasiconvex mapping in a separated topological linear space.

Strong Convergence Theorems for Asymptotically Strictly Pseudocontractive Maps in Hilbert Spaces

The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive maps in Hilbert spaces to have strong convergence. Our results extend those of Kim, Xu, Nakajo, Takahashi and many others.

Hilbert空间中广义平衡问题与k-严格伪压缩映象的强收敛定理

在Hilbert空间中引进并研究了一种新的迭代算法,借以寻求广义平衡问题解集与k-严格伪压缩映象不动点集的一公共元.所得到的结果,推广并改进了最近一些人所发布的新结果.

集值映射向量优化问题的严有效性

将严有效性概念推广到集值映射向量优化问题，并较为系统地研究了它的性质，获得了有关标量化、 Ｌａｇｒａｎｇｅ 乘子、 Ｌａｇｒａｎｇｅ 型对偶及严有效点集的连通性。

Hilbert空间中闭的拟严格伪压缩映像的收缩投影方法(英文)

在Hilbert空间中,引入和研究了一种新的收缩投影迭代算法,用以逼近拟严格伪压缩映像的不动点.在适当的条件下,利用所提出的收缩投影算法证明了闭的拟严格伪压缩映像的不动点的强收敛定理,所得结果改进和推广了近期文献的相关结果.

广义平衡问题与无限族k-严格伪压缩映象的强收敛定理

在Hilbert空间中,大多数学者对平衡问题、非扩张映象不动点的问题做了广泛研究.在Hilbert空间的框架下,讨论了广义平衡问题的解集与无限族k-严格伪压缩映象公共不动点集公解的问题,给出了一个新的迭代序列,并在适当的条件下,用黏性逼近的方法,证明了一些强收敛定理.结果也推广和改进了最近一些人的主要结果.

具有集值映射变分不等式的理论分析

在无穷维自反Banach空间中,介绍具有集值映射的变分不等式几个主要问题的研究进展.介绍如何将变分不等式等价地转化为最小化问题和非光滑的非线性方程问题,及各种转化方式的优势和不足.当变分不等式模型中的集合无界时,许多学者研究了各种各样的强制性条件,以保证变分不等式的解存在.比较几种主要强制性条件之间的关系,并在映射具有伪单调或者拟单调性质时,讨论与变分不等式解集非空/非空有界等价的强制性条件.严格可行性是变分不等式内点算法中需要的主要假设,在映射是伪单调时讨论了解集非空有界与严格可行性之间的关系.变分不等式孤立解的扰动分析被广泛研究,有很多专著介绍这方面的工作,而对整个解集的扰动分析的结果却很少.在映射具有伪单调性的条件下,介绍了变分不等式解集扰动分析的最新进展,Tikhonov正则化也被放在扰动分析的框架下讨论.另外,一些值得进一步研究的问题也被提及.

Hilbert空间中严格伪压缩映像族公共不动点的迭代算法

给出了Hilbert空间中严格伪压缩映像族公共不动点的一个新的迭代算法,并利用所给出的算法证明了一个强收敛定理.

党内法规研究的现状、热点及趋势——基于CNKI期刊(1992—2018年)的文献计量分析

近些年,国内形成了党内法规研究的热潮,亟须对相关研究予以梳理与总结,以推进党内法规研究向纵深拓展。以1992—2018年CNKI收录的565篇北大核心和南大核心(CSSCI含扩展版)有关党内法规的期刊论文数据为样本,利用可视化分析软件Cite Space绘制知识图谱,可以辅助分析国内党内法规研究的现状、热点和发展趋势。研究发现,国内党内法规研究在2013年之后出现爆发式增长态势;党建、法学和政治学领域的学者、期刊和机构构成了主体支持力量;党内法规的概念与意义、党内法规制度体系建设路径、党内法规与国家法律衔接与协调是主要热点议题;跨学科研究、经验研究方法、具体化和技术性研究是其薄弱环节。未来研究需围绕党内法规基础理论、具体化研究和技术性研究等方面深化党内法规研究。