Existence of fixed points of nonexpansive mappings satisfying the Rothe condition

In this paper we consider the following situation: H is a Hilbert space, A is a nonempty bounded closed (not necessarily convex) subset of H, f:D HH is a nonexpansive mapping and A D. In the basic result (Theorem 1) it is shown that in this situation the nonexpansive map f has a fixed point in A, if f satisfies the Rothe condition on A:f(A)A.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 122, pp. 5–12, 1982.     

Approximating fixed points of Suzuki-generalized nonexpansive mappings

In this paper, we prove weak and strong convergence theorems for Ishikawa iteration of Suzuki-generalized nonexpansive mappings in uniformly convex Banach spaces. Furthermore, we extend the results to CAT(0) spaces. Our work extends the results of Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mapping, J. Math. Anal. Appl. 340 (2008) 1088–1095] and Takahashi and Kim [W. Takahashi, G.E. Kim, Approximating fixed points of nonexpansive mappings in Banach spaces, Math. Jpn. 48 (1998) 1–9].     

Approximating fixed points of holomorphic mappings in the Hilbert ball

We approximate fixed points of holomorphic and ρ-nonexpansive self-mappings of the Hilbert ball using both continuous and discrete schemes.     

Approximating common fixed points of nearly asymptotically nonexpansive mappings

We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings.We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansive mappings and those of [9] not only to a larger class of mappings but also with better rate of convergence.     

三个渐进非扩张映象对公共不动点的逼近问题

研究Banach空间中三个渐进非扩张映象对公共不动点的逼近问题.本文结果发展和改进了最近一些人的最新结果.     

逼近一致凸Banach空间中渐近非扩张映象的不动点

借助于B ruck′s不等式,研究了一致凸Banach空间中渐近非扩张映象不动点的具误差的Ish ikaw a迭代序列的强收敛定理.所得的结果推广和改进了Schu,Rhoades,周海云,王绍荣等作者的相应结果.     

Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections

In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [S. Matsushita, W. Takahashi, Approximating fixed points of nonexpansive mappings in a Banach space by metric projections, Appl. Math. Comput. 196 (2008) 422–425] which was established for nonexpansive mappings.     

Approximating common fixed points of asymptotically nonexpansive mappings by composite algorithm in Banach spaces

Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E. Let T ₁, T ₂ and T ₃: K → E be asymptotically nonexpansive mappings with {k _n }, {l _n } and {j _n }. [1, ∞) such that Σ _n=1 ^∞ (k _n − 1) < ∞, Σ _n=1 ^∞ (l _n − 1) < ∞ and Σ _n=1 ^∞ (j _n − 1) < ∞, respectively and F nonempty, where F = {x ∈ K: T _1x = T _2x = T ₃ x} = x} denotes the common fixed points set of T ₁, _{T 2} and T ₃. Let {α _n }, {α′ _n } and {α″ _n } be real sequences in (0, 1) and ∈ ≤ {α _n }, {α′ _n }, {α″ _n } ≤ 1 − ∈ for all n ∈ N and some ∈ > 0. Starting from arbitrary x ₁ ∈ K define the sequence {x _n } by

Common fixed point theorems for mappings satisfying property (E.A) on cone metric spaces

The aim of this paper is to give some new common fixed point theorems for mappings satisfying property (E.A) on cone metric spaces. And we prove the existence and uniqueness of solution for a ordinary differential equation with periodic boundary condition.     

New fixed point theorems of condensing mappings satisfying the interior condition in Banach spaces

In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Altman’s theorem, Roth’s theorem and Petryshyn’s theorem are extended to condensing mappings satisfying the interior condition.     

Common fixed point theorem for noncommuting mappings satisfying a generalized asymptotically nonexpansive condition

We present a common fixed point theorem for generalized asymptotically nonexpansive and noncommuting mappings in normed linear spaces.      

Approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces

In this paper, we consider an Ishikawa type iteration process with errors, which converges to the unique common fixed point of a pair of contractive type mappings in complete generalized convex metric spaces. Furthermore, we obtain the corresponding results in Banach spaces. Our results extend and generalize many known results.     

Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces

In this paper, a kind of Ishikawa type iterative scheme with errors for approximating a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings is introduced and studied in convex metric spaces. Under some suitable conditions, the convergence theorems concerned with the Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings were proved in convex metric spaces. The results presented in the paper generalize and improve some recent results of Wang and Liu (C. Wang, L.W. Liu, Convergence theorems for fixed points of uniformly quasi-Lipschitzian mappings in convex metric spaces, Nonlinear Anal., TMA 70 (2009), 2067-2071).     

(渐近)非扩张映象的不动点的迭代逼近

Let E be a uniformly convex Banach space which satisfies Opial‘s condition or has aFrechet differentiable norm,and C be a bounded closed convex subset of E. If T： C→C is(asymptotically)nonexpansive,then the modified Ishikawa iteration process defined by     

Approximating common fixed points of Lipschitzian pseudocontraction semigroups

In this paper, we prove a weak convergence theorem of the implicit iteration process for the semigroups of Lipschitz pseudocontractive mappings in uniformly convex Banach spaces with the Opial property.