Banach空间上非Lipschitz映射的渐近行为

设Ｃ是具Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间Ｅ的非空凸闭子集，Ｇ是定向集．｛Ｔ_ｔ：ｔ∈Ｇ｝是Ｃ上的渐近非扩张型映照．本文给出了｛Ｔ_ｔ：ｔ∈Ｇ｝的弱收敛定理．     

一致凸Banach空间中渐近非扩张映象的几乎轨道的渐近行为

设Ｘ是有Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间，Ｃ是Ｘ的有界闭凸子集，Ｔ：Ｃ→Ｃ是一个渐近非扩张映象．证明了，如果｛ｘ_ｎ：ｎ≥１｝是Ｔ的几乎轨道，则序列｛ｘ０｝弱几乎收敛到集合∩from∞to(ｎ＝１)ｃｏ｛ｘ_i：ｉ≥ｎ｝∩Ｆ（Ｔ）的唯一点，其中，Ｆ（Ｔ）是Ｔ的不动点集．     

Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings

Let be a real Banach space with a uniformly Gâteaux differentiable norm possessing uniform normal structure, be a nonempty closed convex and bounded subset of , be an asymptotically nonexpansive mapping with sequence . Let be fixed, be such that , , and . Define the sequence iteratively by , n= 0, 1, 2, ..._. $"> It is proved that, for each integer , there is a unique such that If, in addition, and , then converges strongly to a fixed point of .

     

Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals

In this paper, we prove Krasnoselskii and Mann's type convergence theorems for nonexpansive semigroups without using Bochner integral and without assuming the strict convexity of Banach spaces. One of our main results is the following: let C be a compact convex subset of a Banach space E and let be a one-parameter strongly continuous semigroup of nonexpansive mappings on C. Let {tn} be a sequence in [0,∞) satisfying

     

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.     

On the convergence of modified Noor iterations with errors for asymptotically nonexpansive mappings

In this paper, several weak and strong convergence theorems are established for a modified Noor iterative scheme with errors for three asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type, and Noor-type iterations are covered by the new iteration scheme. Our results extend and improve the recently announced ones [B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453; Y.J. Cho, H. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004) 707-717] and many others.     

The Domínguez–Lorenzo condition and multivalued nonexpansive mappings

Let E be a nonempty bounded closed convex separable subset of a reflexive Banach space X   which satisfies the Domínguez–Lorenzo condition, i.e., an inequality concerning the asymptotic radius of a sequence and the Chebyshev radius of its asymptotic center. We prove that a multivalued nonexpansive mapping T:E→2^X$T:E\to 2^X$ which is compact convex valued and such that T(E)$T(E)$ is bounded and satisfies an inwardness condition has a fixed point. As a consequence, we obtain a fixed-point theorem for multivalued nonexpansive mappings in uniformly nonsquare Banach spaces which satisfy the property WORTH, extending a known result for the case of nonexpansive single-valued mappings. We also prove a common fixed point theorem for two nonexpansive commuting mappings t:E→E$t:E\to E$ and T:E→KC(E)$T:E\to \mathit{KC}(E)$ (where KC(E)$\mathit{KC}(E)$ denotes the class of all compact convex subsets of E) when X is a uniformly convex Banach space.