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 ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

In this article, we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces. The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.     

Iterative Algorithm with Mixed Errors for Solving a New System of Generalized Nonlinear Variational-Like Inclusions and Fixed Point Problems in Banach Spaces

A new system of generalized nonlinear variational-like inclusions involving Amaximal m-relaxed η-accretive(so-called,(A, η)-accretive in [36]) mappings in q-uniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings due to Lan et al., the existence and uniqueness of a solution to the aforementioned system is established. Applying two nearly uniformly Lipschitzian mappings S1 and S2 and using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings, we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q =(S1, S2) which is the unique solution of the aforesaid system. We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions. The results presented in this paper extend and improve some known results in the literature.     

Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces

This paper studies the convergence of the sequence defined by x0∈C,xn 1=αnu (1-αn)Txn,n=0,1,2,…, where 0 ≤αn ≤ 1, limn→∞αn = 0, ∑∞n=0 αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.     

Modified block iterative method for solving convex feasibility problem,equilibrium problems and variational inequality problems

The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-φ-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem (CFP) and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.     

The average errors for Hermite-Fejr interpolation on the Wiener space

For 1≤ p ∞, firstly we prove that for an arbitrary set of distinct nodes in [-1, 1], it is impossible that the errors of the Hermite-Fejr interpolation approximation in L p -norm are weakly equivalent to the corresponding errors of the best polynomial approximation for all continuous functions on [-1, 1]. Secondly, on the ground of probability theory, we discuss the p-average errors of Hermite-Fejr interpolation sequence based on the extended Chebyshev nodes of the second kind on the Wiener space. By our results we know that for 1≤ p ∞ and 2≤ q ∞, the p-average errors of Hermite-Fejr interpolation approximation sequence based on the extended Chebyshev nodes of the second kind are weakly equivalent to the p-average errors of the corresponding best polynomial approximation sequence for L q -norm approximation. In comparison with these results, we discuss the p-average errors of Hermite-Fejr interpolation approximation sequence based on the Chebyshev nodes of the second kind and the p-average errors of the well-known Bernstein polynomial approximation sequence on the Wiener space.     

ITERATIVE APPROXIMATION OF FIXED POINTS OF NON-LIPSCHITZIAN ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS

The purpose of this paper is to investigate the problem of approximating fixed points of non-Lipschitizian asymptotically pseudocontractive mappings in an arbitrary real Banach space by the modified Ishikawa iterative sequences with errors.     

Necessary and sufficient condition of the strong convergence for two finite families of uniformly L-Lipschitzian mappings

The purpose of this paper is to study necessary and su?cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2-7].     

FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS

The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ? of the split feasibility problem and the set F(T)of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of puniformly convex Banach spaces which are also uniformly smooth.By combining Mann's iterative method and the Halpern's approximation method,we propose an iterative algorithm for finding an element of the set F(T) ∩ ?;moreover,we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method.Our results extend and complement many known related results in the literature.     

Strong Convergence Theorems for a Family of Quasi-φ-Asymptotically Nonexpansive Mappings

The purpose of this article is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-asymptotically nonexpansive mappings.Its results hold in reflexive,strictly convex,smooth Banach spaces with the property(K).The results of this paper improve and extend recent some relative results.     

Banach空间中带误差的修改的Ishikawa迭代程序

本文研究在任意的实Banach空间中用带误差的修改的Ishikawa迭代序列来逼近一致Lipschitz的渐近伪压缩映象的不动点的问题.在去掉限制limn→∞βn=0之下,证明了张石生教授的结果(见文[1])仍真.另一方面,也把他的结果推广到了带误差的修改的Ishikawa迭代序列的情形.     

Banach空间中渐近拟非扩展型映象不动点的迭代逼近

本文研究了一致凸Banach空间中渐近拟非扩展型映象和渐近非扩展型映象T的不动点的迭代逼近问题.利用范数不等式，在去掉[3]中一个较强条件的情况下，证明了T的具误差的Ishikawa迭代序列中收敛于T的某个不动点.所得定理推广和改进了已有的部分结果。     

Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings

Some convergence theorems of modified Ishikawa and Mann iterative sequences with errors for asymptotically pseudo-contractive and asymptotically nonexpansive mappings in Banach space are obtained. The results presented in this paper improve and extend the corresponding results in Goebel and Kirk (1972), Kirk (1965), Liu (1996), Schu (1991) and Chang et al. (to appear).

     

Banach空间中渐近拟非扩张型映象迭代序列的稳定性

本文研究了一类涉及渐近拟非扩张型映象的带误改进Mann迭代序列,利用Tan和Xu的不等式,得到了该带误差Mann迭代序列的稳定性,推广了其他人的结果.     

凸度量空间中拟压缩映象具误差的Ishikawa型迭代序列的收敛性

对凸度量空间中非线性拟压缩映象具误差的Ishikawa型迭代序列的收敛性问题证明了几个新的收敛性定理，结果不仅改进和推广了L.B.Ciric,Q.H.Lin,H.E.Rhoades,H.K.Xu等人的相应结果，而且对Rhoades-Naimplally-Singh所提出的公开问题，在凸度量空间的框架下给出了肯定的答复。     

Banach空间中严格渐近伪压缩映象的收敛性问题

在一致凸的Banach空间中，采用新的证明方法研究了严格渐近伪压缩映象和渐近非膨胀映象带误差的修正的Mann和Ishikawa迭代程序的收敛性问题，不要求定义域、值域有界，且迭代系数更简单．     

关于渐近伪压缩型映象的不动点的迭代构造

本文引入了Banach空间中一类渐近伪压缩型映象,它概括了熟知的若干映象类成特例.而且,还研究了关于这类映象的带误差的修改了的Ishikawa与Mann迭代序列的逼近问题.本文所得结果改进与推广了张石生教授的所有结果以及前人研究的相应结果.     

渐近拟非扩张型映象的Ishikawa迭代序列的强收敛性

通过引入一新型条件,研究了渐近拟非扩张型映象不动点的具误差的修正的Ish ikaw a迭代序列的迭代逼近问题,得到新的结果.     

Φ-伪压缩映象带混合型误差的迭代序列的强稳定性

引入带混合型误差的 Ishikawa和 Mann迭代序列 ,在没有 D是有界闭集与多值映象 T是一致连续的较弱条件下 ,在实 Banach空间中研究了多值Φ -伪压缩映象不动点的带混合型误差的 Ishikawa和 Mann迭代序列的逼近问题 ,使用与文献完全不同的方法 ,建立了带混合型误差的 Ishikawa和 Mann迭代序列的强稳定性定理 ,从而统一和发展了几位作者早期与最近的相关结果 .     

Banach空间中带误差修改的不动点迭代逼近

对Banach空间中一致L-Lipschitz映射带误差修改的Ishikawa迭代序列和带误差的修改的Mann迭代序列强收敛的充要条件进行了研究,所得结果改进和推广了最近文献中的一些相应结果.