Banach空间中有限个一致李普希兹渐近伪压缩映射的强收敛定理

目的是把对单个渐近T为压缩映射的迭代结果推广到有限个渐近T为压缩映射上.为此,利用数学归纳法的思想,在一定条件下,得出了有限个渐近T为压缩映射强收敛于其公共不动点的结论.此结论推广了以前的结果.     

渐近半伪压缩映射的收敛性定理及其应用(英文)

本文在一致凸的Banach空间中研究一致L-Lipshitzian渐近半伪压缩映射的带平均误差的三步迭代序列.应用新的方法,得到一致L-Lipshitzian渐近半伪压缩映射的一些强收敛的充分必要条件,改进和推广了文[4]中相应的结果.     

郭氏定理的再推广

本文研究了严格集压缩映射、凝聚映射的拓扑度,给出了拓扑度为零的充分条件,从而得到严格集压缩映射,凝聚映射,半紧Ⅰ集压缩映射的不动点定理。本文的结论推广和改进了有关郭大钩定理的若干已知结果。     

压缩映射定理的相关结论

文中主要探讨了压缩映射定理的相关结论,并给出了这些结论的证明.     

伪压缩和单调映射迭代法的强收敛定理(英文)

本文在Hilbert空间中研究有限个伪压缩映射,严格伪压缩映射和单调映射产生的变分不等式的迭代算法,获得伪压缩映射不动点集和变分不等式解的公共元素的强收敛定理,扩展了许多作者的相关研究.     

关于压缩映射与扩张映射不动点问题的迭代算法［英文］

本文给出Hilbert空间与Banach空间中关于压缩映射、扩张映射的若干迭代格式,证明这些映射的不动点集与均衡问题解集的强(弱)收敛定理,本文改进和推广了相关文献中的结果.     

关于Lipschitzian伪压缩映射的合成隐迭代序列(英文)

本文研究了Lipschitzian伪压缩映射的合成隐迭代序列.利用伪压缩映射等价不等式,在Banach空间中,得到了合成隐迭代序列强收敛的充分必要条件,推广了一些相关的结果.     

WF-模糊度量空间中的不动点理论

在WF-模糊度量空间中建立压缩型和局部压缩型映射的不动点理论，推广一些重要的不动点定理。     

Banach空间中α-序压缩映射的不动点定理

在Banach空间中引入了几种压缩映射,证明了一类非线性映射的不动点的存在性,并改进和推广了相应定理.     

有限个渐近伪压缩映射近迫点序列的收敛性

研究了Banach空间中有限个渐近伪压缩映射近迫点序列的收敛性问题,此结果推广了以前的结论.     

关于非扩张映象的最近的公共不动点问题

利用粘性逼近方法,在自反Banach空间的框架下,研究无限族非扩张映象及对给定的压缩映象的迭代程序的收敛性问题．在适当的条件下,证明了该迭代序列强收敛于某一公共不动点,而且这一公共不动点也是自反Banach空间中某一变分不等式的唯一解．所得结果改进和推广了一些人的最新的结果．     

Stability and convergence of modified Ishikawa iterative sequences with errors in Banach spaces

Summary Some stability and convergence theorems of the modified Ishikawa iterative sequences with errors for asymptotically nonexpansive mapping in the intermediate sense and asymptotically pseudo contractive and uniformly Lipschitzian mappings in Banach spaces are obtained.     

G-锥度量空间中压缩映射的不动点定理

给出了G-锥度量空间的概念,利用迭代法探究了G-锥度量空间中压缩映射不动点定理,证明了在G-锥度量空间中锥没有正规性的条件下压缩映射存在唯一不动点.     

Kannan压缩映像的逆问题

称空间(X,d)上的自映像f为Kannan压缩映像,若对于,成立d(f(x),f(y))≤a{d(x,f(x))+d(y,f(y)}, 其中0<α<1/2。 Kannan压缩映像是Banach压缩映像的重要推广,特别在Banach压缩映像已被许多作者推广为形式多样的情况下(例如见[8],那里归纳出250个压缩映像定义),重要性尤其突出。本文通过对Kannan压缩映像逆问题的证明,把相当一部分形式不同的压缩映像统一归并为Kannan压缩映像。     

关于带扰动映像的广义平衡问题与k-严格伪压缩映像的不动点问题的强收敛定理

在Hilbert空间中提出一种新的迭代算法,用于寻求带扰动映像的广义平衡问题与k-严格伪压缩映像的不动点问题的公共解.此外,证明了由此迭代算法生成的序列的强收敛性.所得到的结果,推广并改进了最近一些人所发布的新结果.     

公共不动点定理

本文在Ｈａｕｓｄｏｒｆｆ一致度量空间上首先定义了偏序 ,再利用Ｋｎａｓｔｅｒ－Ｔａｒｓｋｉ原理建立了广义压缩映射的公共不动点定理．     

Generalized multivalued nonlinear quasivariational inclusions

In this paper, we introduce and study a few classes of generalized multivalued nonlinear quasivariational inclusions and generalized nonlinear quasivariational inequalities, which include many classes of variational inequalities, quasivariational inequalities and variational inclusions as special cases. Using the resolvent operator technique for maximal monotone mapping, we construct some new iterative algorithms for finding the approximate solutions of these classes of quasivariational inclusions and quasivariational inequalities. We establish the existence of solutions for this generalized nonlinear quasivariational inclusions involving both relaxed Lipschitz and strongly monotone and generalized pseudocontractive mappings and obtain the convergence of iterative sequences generated by the algorithms. Under certain conditions, we derive the existence of a unique solution for the generalized nonlinear quasivariational inequalities and obtain the convergence and stability results of the Noor type perturbed iterative algorithm. The results proved in this paper represent significant refinements and improvements of the previously known results in this area.     

带扰动映像的广义平衡问题和不动点问题的混合粘性逼近问题

引入一个用于寻求带扰动映像的广义平衡问题解集以及可数无穷多非扩张映像之族公共不动点集的公共解的新的迭代算法. 证明了由此算法生成的序列的强收敛性. 所得的结果推广改进了先前许多作者的结果.     

Picard’s iterative method for nonlinear advection-reaction-diffusion equations

Picard’s iterative method for the solution of nonlinear advection-reaction-diffusion equations is formulated and its convergence proved. The method is based on the introduction of a complete metric space and makes uses of a contractive mapping and Banach’s fixed-point theory. From Picard’s iterative method, the variational iteration method is derived without making any use at all of Lagrange multipliers and constrained variations. Some examples that illustrate the advantages and shortcomings of the iterative procedure presented here are shown.     

SOME NEW ITERATED FUNCTION SYSTEMS CONSISTING OF GENERALIZED CONTRACTIVE MAPPINGS

Iterated function systems (IFS) were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle.In 2010,D.R.Sahu and A.Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings.In this paper,following Hutchinson,D.R.Sahu and A.Chakraborty,we present some new iterated function systems by using the so-called generalized contractive mappings,which will also cover a large range of mappings.Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.