共查询到20条相似文献,搜索用时 46 毫秒
1.
Let K be a nonempty closed convex subset of a Banach space E, T:K→K a continuous pseudo-contractive mapping. Suppose that {αn} is a real sequence in [0,1] satisfying appropriate conditions; then for arbitrary x0∈K, the Mann type implicit iteration process {xn} given by xn=αnxn−1+(1−αn)Txn,n≥0, strongly and weakly converges to a fixed point of T, respectively. 相似文献
2.
Let C be a closed convex subset of a real Hilbert space H and assume that T is an asymptotically κ-strict pseudo-contraction on C with a fixed point, for some 0≤κ<1. Given an initial guess x0∈C and given also a real sequence {αn} in (0, 1), the modified Mann’s algorithm generates a sequence {xn} via the formula: xn+1=αnxn+(1−αn)Tnxn, n≥0. It is proved that if the control sequence {αn} is chosen so that κ+δ<αn<1−δ for some δ∈(0,1), then {xn} converges weakly to a fixed point of T. We also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence. 相似文献
3.
Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm, let K be a nonempty closed convex subset of E, and let T:K?E be a continuous pseudocontraction which satisfies the weakly inward condition. For f:K?K any contraction map on K, and every nonempty closed convex and bounded subset of K having the fixed point property for nonexpansive self-mappings, it is shown that the path x→xt,t∈[0,1), in K, defined by xt=tTxt+(1−t)f(xt) is continuous and strongly converges to the fixed point of T, which is the unique solution of some co-variational inequality. If, in particular, T is a Lipschitz pseudocontractive self-mapping of K, it is also shown, under appropriate conditions on the sequences of real numbers {αn},{μn}, that the iteration process: z1∈K, zn+1=μn(αnTzn+(1−αn)zn)+(1−μn)f(zn),n∈N, strongly converges to the fixed point of T, which is the unique solution of the same co-variational inequality. Our results propose viscosity approximation methods for Lipschitz pseudocontractions. 相似文献
4.
5.
6.
It is proved that the modified Mann iteration process: xn+1=(1−αn)xn+αnTnxn,n∈N, where {αn} is a sequence in (0, 1) with δ≤αn≤1−κ−δ for some δ∈(0,1), converges weakly to a fixed point of an asymptotically κ-strict pseudocontractive mapping T in the intermediate sense which is not necessarily Lipschitzian. We also develop CQ method for this modified Mann iteration process which generates a strongly convergent sequence. 相似文献
7.
Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
8.
9.
We show strong and weak convergence for Mann iteration of multivalued nonexpansive mappings T in a Banach space. Furthermore, we give a strong convergence of the modified Mann iteration which is independent of the convergence of the implicit anchor-like continuous path zt∈tu+(1−t)Tzt. 相似文献
10.
Let T:D⊂X→X be an iteration function in a complete metric space X. In this paper we present some new general complete convergence theorems for the Picard iteration xn+1=Txn with order of convergence at least r≥1. Each of these theorems contains a priori and a posteriori error estimates as well as some other estimates. A central role in the new theory is played by the notions of a function of initial conditions of T and a convergence function of T. We study the convergence of the Picard iteration associated to T with respect to a function of initial conditions E:D→X. The initial conditions in our convergence results utilize only information at the starting point x0. More precisely, the initial conditions are given in the form E(x0)∈J, where J is an interval on R+ containing 0. The new convergence theory is applied to the Newton iteration in Banach spaces. We establish three complete ω-versions of the famous semilocal Newton–Kantorovich theorem as well as a complete version of the famous semilocal α-theorem of Smale for analytic functions. 相似文献
11.
We show that the equality m1(f(x))=m2(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps, f(a)=g(a)=0 and m1,m2 are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between f and g is obtained. 相似文献
12.
Let K be a compact convex subset of a real Hilbert space H; T:K→K a hemicontractive map. Let {αn} be a real sequence in [0,1] satisfying appropriate conditions; then for arbitrary x0∈K, the sequence {xn} defined iteratively by xn=αnxn−1+(1−αn)Txn, n≥1 converges strongly to a fixed point of T. 相似文献
13.
Under the assumption that E is a reflexive Banach space whose norm is uniformly Gêteaux differentiable and which has a weakly continuous duality mapping Jφ with gauge function φ, Ceng–Cubiotti–Yao [Strong convergence theorems for finitely many nonexpansive mappings and applications, Nonlinear Analysis 67 (2007) 1464–1473] introduced a new iterative scheme for a finite commuting family of nonexpansive mappings, and proved strong convergence theorems about this iteration. In this paper, only under the hypothesis that E is a reflexive Banach space which has a weakly continuous duality mapping Jφ with gauge function φ, and several control conditions about the iterative coefficient are removed, we present a short and simple proof of the above theorem. 相似文献
14.
Mehmet Özer Yasar Polatoglu Gürsel Hacibekiroglou Antonios Valaristos Amalia N. Miliou Antonios N. Anagnostopoulos Antanas Čenys 《Nonlinear Analysis: Theory, Methods & Applications》2008
The dynamic behaviour of the one-dimensional family of maps f(x)=c2[(a−1)x+c1]−λ/(α−1) is examined, for representative values of the control parameters a,c1, c2 and λ. The maps under consideration are of special interest, since they are solutions of the relaxed Newton method derivative being equal to a constant a. The maps f(x) are also proved to be solutions of a non-linear differential equation with outstanding applications in the field of power electronics. The recurrent form of these maps, after excessive iterations, shows, in an xn versus λ plot, an initial exponential decay followed by a bifurcation. The value of λ at which this bifurcation takes place depends on the values of the parameters a,c1 and c2. This corresponds to a switch to an oscillatory behaviour with amplitudes of f(x) undergoing a period doubling. For values of a higher than 1 and at higher values of λ a reverse bifurcation occurs. The corresponding branches converge and a bleb is formed for values of the parameter c1 between 1 and 1.20. This behaviour is confirmed by calculating the corresponding Lyapunov exponents. 相似文献
15.
Bosek and Krawczyk exhibited an on-line algorithm for partitioning an on-line poset of width w into w14lgw chains. They also observed that the problem of on-line chain partitioning of general posets of width w could be reduced to First-Fit chain partitioning of 2w2+1-ladder-free posets of width w, where an m-ladder is the transitive closure of the union of two incomparable chains x1≤?≤xm, y1≤?≤ym and the set of comparabilities {x1≤y1,…,xm≤ym}. Here, we provide a subexponential upper bound (in terms of w with m fixed) for the performance of First-Fit chain partitioning on m-ladder-free posets, as well as an exact quadratic bound when m=2, and an upper bound linear in m when w=2. Using the Bosek–Krawczyk observation, this yields an on-line chain partitioning algorithm with a somewhat improved performance bound. More importantly, the algorithm and the proof of its performance bound are much simpler. 相似文献
16.
Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
17.
Let X be a uniformly smooth Banach space, C be a closed convex subset of X, and A an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn} by the algorithm
where αn and γn are two sequences satisfying certain conditions, Jr denotes the resolvent (I+rA)−1 for r>0, and f:C→C be a fixed contractive mapping. Then as n→∞, the sequence {xn} strongly converges to a point in F(A). The results presented extends and improves the corresponding results of Hong-Kun Xu [Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643]. 相似文献
xn+1=αnf(xn)+(1−αn)Jrnxn,
18.
We study the bounded regions in a generic slice of the hyperplane arrangement in Rn consisting of the hyperplanes defined by xi and xi+xj. The bounded regions are in bijection with several classes of combinatorial objects, including the ordered partitions of [n] all of whose left-to-right minima occur at odd locations and the drawings of rooted plane trees with n+1 vertices. These are sequences of rooted plane trees such that each tree in a sequence can be obtained from the next one by removing a leaf. 相似文献
19.
We consider the Mosco convergence of the sets of fixed points for one-parameter strongly continuous semigroups of nonexpansive mappings. One of our main results is the following: Let C be a closed convex subset of a Hilbert space E. Let {T(t):t≥0} be a strongly continuous semigroup of nonexpansive mappings on C. The set of all fixed points of T(t) is denoted by F(T(t)) for each t≥0. Let τ be a nonnegative real number and let {tn} be a sequence in R satisfying τ+tn≥0 and tn≠0 for n∈N, and limntn=0. Then {F(T(τ+tn))} converges to ?t≥0F(T(t)) in the sense of Mosco. 相似文献
20.
Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are bounded strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. A new explicit coupled iteration process is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献