Viscosity approximation with weak contractions for fixed point problem,equilibrium problem,and variational inequality problem

This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.（Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715（2009））,Plubtieng and Punpaeng（Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469（2007））,Colao et al.（Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352（2008））,Yao et al.（Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363（2007）DOI 10.1155/2007/64363）,and others.

Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions

Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems.It is known that many problems in applied sciences and engineering can be formulated as functional equations.Such equations can be transferred to fixed point theorems in an easy manner.Moreover,we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations.Let X be a non-empty set.A fixed point for a self-mapping T on X is a point𝑒𝑒∈𝑋𝑋that satisfying T e=e.One of the most challenging problems in mathematics is to construct some iterations to faster the calculation or approximation of the fixed point of such problems.Some mathematicians constructed and generated some new iteration schemes to calculate or approximate the fixed point of such problems such as Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Berinde(2004b);Agarwal,O’Regan and Sahu(2007)].The main purpose of the present paper is to introduce and construct a new iteration scheme to calculate or approximate the fixed point within a fewer number of steps as much as we can.We prove that our iteration scheme is faster than the iteration schemes given by Sintunavarat et al.[Sintunavarat and Pitea(2016);Agarwal,O’Regan and Sahu(2007);Mann(1953);Ishikawa(1974)].We give some numerical examples by using MATLAB to compare the efficiency and effectiveness of our iterations scheme with the efficiency of Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Abbas and Nazir(2014);Agarwal,O’Regan and Sahu(2007)]schemes.Moreover,we introduce a problem raised from Newton’s law of cooling as an application of our new iteration scheme.Also,we support our application with a numerical example and figures to illustrate the validity of our iterative scheme.

Endpoints of Multi-Valued Weak Contractions on the Metric Space of Partially Ordered Groups

The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively;and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).

On Almost Type α-F-Z-Weak Contraction in Metric Spaces

In this article, we introduce a new type of contraction named almost type α-F-Z-weak contraction, which comes from a combination of F-contraction, Z-contraction, and almost contraction, and then we provide sufficient conditions for the existence and uniqueness of fixed point of such contractions in complete metric spaces and give some related fixed point results. In addition, some related fixed point results can derive from our main results.

Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings

Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.

COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized （ψ, Ф）-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.

Unique Common Fixed Points for Two Weakly C~*-contractive Mappings on Partially Ordered 2-metric Spaces

In this paper, we give existence theorems of common fixed points for two mappings with a weakly C*-contractive condition on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point.

Fixed Point Curve for Weakly Inward Contractions and Approximate Fixed Point Property

In this paper, we discuss the concept of fixed point curve for linear interpolations of weakly inward contractions and establish necessary condition for a nonex- pansive mapping to have approximate fixed point property.

马来酸麦角新碱联合缩宫素对宫缩乏力产后出血产妇的临床分析

目的探讨产后宫缩乏力产后出血采用马来酸麦角新碱联合缩宫素治疗的效果与应用价值。方法选取76例宫缩乏力产后出血产妇,按照手环编号单双情况分为两组,每组38例。对照组(手环编号单数)单纯予以缩宫素治疗,观察组(手环编号双数)采用马来酸麦角新碱联合缩宫素治疗,对比两组治疗效果。结果观察组产妇治疗总有效率高于对照组(P<0.05)。观察组产妇产后1h、2h、12h、24h出血量均少于对照组(P<0.05)。结论产妇产后因宫缩乏力诱发产后出血可基于缩宫素基础上联合马来酸麦角新碱治疗,相比单独用药治疗效果更明显,可有效减少出血量,值得临床推广。

Banach空间中广义投影变形迭代法的收敛性

在Banach空间中,应用新的广义投影方法和变形的逐次逼近方法以及变形的Mann迭代序列方法,研究了渐近弱压缩非自映象T:G→B的不动点迭代过程的强收敛性.其结果推广了一些最近相应的结果,其方法不同于其他作者的方法.

上市公司内部控制实质性缺陷与债务融资约束

以2007～2011年非金融类上市公司数据为依据,结果内部控制实质性缺陷对债务融资约束的影响.结果发现,当公司存在内部控制实质性缺陷时,债务期限较短,债务成本较高,新增借款能力较差;内部控制实质性缺陷还会对公司的债务融资产生长期的不利影响.

卡贝缩宫素在预防和治疗剖宫产术中术后出血的临床研究

目的观察卡贝缩宫素预防与治疗剖宫产术中术后出血的疗效。方法 210例有产后出血倾向的孕妇随机分为观察组与对照组,观察组160例术中预防使用卡贝缩宫素,对照组50例常规使用缩宫素,比较两组术中及术后24h出血量。结果观察组术中出血量、24h出血量、产后出血发生率均明显低于对照组(P<0.01)。结论卡贝缩宫素预防与治疗剖宫产术中术后出血疗效显著。

不动点问题平衡问题及变分不等式问题的具弱压缩的粘性逼近

借助具弱压缩的粘性逼近,提出一种新的修正的迭代算法,用以寻求一公共元,它既是一无穷族非扩张映像的公共不动点集中的点,也是一有限族的平衡问题的解集中的点,而且它还是一变分不等式的解.在适当的条件下,一些强收敛定理在Hilbert空间的框架下被建立.所得结果推广和改进了Colao等[Nonlinear Anal,2009,71:2708-2715],Plubtieng等[JMath Anal Appl,2007,336:455-469],Colao等[JMath Anal Appl,2008,344:340-352],Yao等[Fixed Point Theory Appl,2007,ArtID64363]及其他人的一些最新的结果.

自适应遗传算法

在遗传算法中约束条件贯穿于遗传运算的始终,这样必定影响运算效率。因为随着进化过程的进行,适应度较低的一些个体逐渐被淘汰,而适应度较高的个体越来越多,且都集中在最优点附近。基于遗传算法这种优胜劣汰的进化思想,该文提出一种改进的遗传算法——自适应遗传算法。其主要思想是在群体进化若干代后,将弱解空间删除,在以后的进化进程中以同样的群体大小只在强解空间进行群体的繁殖,则可加大强解空间的个体密度,提高解的精度,这样有助于性能优良的个体的产生,并且有可能缩短群体进化过程。将这种自适应遗传算法用于复杂函数的优化,算例结果表明该方法是有效和可靠的。

欣母沛防治乙型肝炎产妇剖宫产产后出血的临床疗效观察

目的:观察欣母沛对防治乙型肝炎产妇剖宫产产后出血的效果和安全性。方法:选择肝功异常但凝血功能正常的乙型肝炎剖宫产产妇300例,随机分为欣母沛组、缩宫素组、联合组(欣母沛加缩宫素),各100例。3组均在胎儿娩出后立即宫体注射药物。比较各组产后2h内及产后24h内的出血量及产后出血率、治疗总有效率。观察各组产妇用药后的不良反应及丙氨酸氨基转移酶(ALT)、门冬氨酸氨基转移酶(AST)、血清总胆红素(TB)变化。结果:欣母沛组及联合组的产后出血发生率分别为22%、20%,明显低于缩宫素组的54%(P<0.01)。两组产后2h、24h平均出血量分别为(271.54±73.96)ml、(360.97±90.12)ml,也明显少于缩宫素组的(368.38±125.41)ml、(486.84±144.35)ml,差异有显著性(P<0.01)。欣母沛组及联合组治疗总有效率96%,明显高于缩宫素组的87%(P<0.05)。用药后缩宫素组ALT、AST、TB较欣母沛组、联合组均有不同程度升高,且ALT、AST的变化有显著差异(P<0.05)。欣母沛组与联合组比较,ALT、AST、TB差异无显著性(P>0.05)。部分产妇出现恶心、呕吐、腹泻、高血压等不良反应,一般均可自行恢复。结论:欣母沛对防治乙型肝炎产妇剖宫产宫缩乏力性产后出血的效果显著,不良反应小,且对肝功能几乎无影响,安全性良好。

欣母沛防治产后出血的临床疗效观察

目的:观察欣母沛预防和治疗产后出血的疗效。方法:50例有产后出血倾向患者,对36例预防性使用催产素及卡前列甲酯栓(卡孕栓),另外14例加用氨丁卡前列素(欣母沛),比较两组产后出血情况;对28例已发生产后出血的患者应用欣母沛,观察疗效。结果:预防性用药组加用欣母沛者产后出血发生率,产后2h、24h平均出血量均明显少于常规用药组;治疗性用药组92.9%有效。结论:欣母沛用于预防及治疗产后出血具有显著疗效。

多重加权移位算子的谱图形、C_(αβ)分类和弱压缩性

本文刻划了复可分Hilbert空间上内射多重加权移位算子的谱图形,讨论了它们的拟三角性质,给出了压缩的内射多重加权移位算子的C_(αβ)分类和多重加权移位算子弱压缩的充要条件。

垄断契约、专用资产与弱势契约主体行为研究——来自烟草种植业的经验数据

通过考察三个乡村的烟草种植业的一个典型契约,发现新制度经济学中的平等自由地签订契约的假设在这里受到了巨大的挑战。我们放松假设,通过对事实上的垄断契约下的弱势契约方的行为分析得出,农民的天然弱势地位决定了只靠农民自身无法签订平等契约,需要借助内部的联合和外力的干预成立经济联合组织才能最大限度实现契约的公平和有效性。

带质心的K最近邻增强模糊最小最大神经网络的集成方法

在分类任务中,传统的模糊最小最大神经网络及其变体在训练网络的时候没有考虑超盒内部训练数据的分布情况,并且考虑扩展系数的问题也不是很充分,导致每次训练新数据集都要重新选择最优的扩展系数。因此,提出了一种带质心的K最近邻增强模糊最小最大神经网络的集成方法。在该方法中,一方面,每个超盒都带有质心,用来描述之前训练的样本在该超盒的大体分布情况,并且在扩展规则及收缩方面考虑了样本距离超盒质心的因素;另一方面,使用5个带质心的K最近邻增强模糊最小最大神经网络作为弱分类器,每个分类器设置不同的扩展系数,当该方法训练完后,将得出的离散属性值作为随机森林的训练集,最后,使用测试样本验证网络的分类性能。实验结果表明:提出的方法在准确率、精准率、召回率以及F-score等方面大部分的结果高于传统的FMMN及其变体的结果,该方法有效地克服了FMMN的准确性过于依赖扩展系数的问题。

开放经济下我国国际工程承包业的SWOT分析与战略选择

开放经济下,我国国际工程承包业发展迅速,本文在研究我国国际工程承包发展现状的基础上,对国际工程承包业的优势、劣势、机遇以及威胁进行了分析,在此基础上提出了推进我国国际工程承包业发展的对策建议。