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101.
Li-ping Yang Xiangsheng Xie Gang Hu 《Journal of Computational and Applied Mathematics》2010,234(4):972-984
A demiclosed principle is proved for asymptotically nonexpansive mappings in the intermediate sense. Moreover, it is proved that the modified three-step iterative sequence converges weakly and strongly to common fixed points of three asymptotically nonexpansive mappings in the intermediate sense under certain conditions. The results of this paper improve and extend the corresponding results of [M.O. Osilike, S.C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Comput. Modelling 32 (2000) 1181-1191; G.E. Kim, T.H. Kim, Mann and Ishikawa iterations with errors for non-Lipschitzian mappings in Banach spaces, Comput. Math. Appl. 42 (2001) 1565-1570; B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453; K. Nammanee, S. Suantai, The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces, Appl. Math. Comput. 187 (2007) 669-679; K. Nammanee, M.A. Noor, S. Suantai, Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 314 (2006) 320-334] and other corresponding known ones. On the other hand, we show the necessary and sufficient condition for the strong convergence of the modified three-step iterative sequence to some common fixed points of . 相似文献
102.
In this article, we first introduce an iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping (assuming existence) and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a nonlinear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method. 相似文献
103.
Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings 总被引:14,自引:0,他引:14
S. S. Chang 《Proceedings of the American Mathematical Society》2001,129(3):845-853
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).
104.
C.E. Chidume 《Journal of Mathematical Analysis and Applications》2003,278(2):354-366
Let K be a nonempty closed convex and bounded subset of a real Banach space E and T:K→K be uniformly L-Lipschitzian, uniformly asymptotically regular with sequence {εn}, and asymptotically pseudocontractive with constant {kn}, where {kn} and {εn} satisfy certain mild conditions. Let a sequence {xn} be generated from x1∈K by xn+1:=(1−λn)xn+λnTnxn−λnθn(xn−x1), for all integers n?1, where {λn} and {θn} are real sequences satisfying appropriate conditions, then ‖xn−Txn‖→0 as n→∞. Moreover, if E is reflexive, and has uniform normal structure with coefficient N(E) and L<N(E)1/2 and has a uniformly Gâteaux differentiable norm, and T satisfies an additional mild condition, then {xn} also converges strongly to a fixed point of T. 相似文献
105.
本文我们证明了Banach空间中渐近拟非扩张映象T的具误差Ishikawa迭代过程收敛到不动点的一个充要条件 ,其中T不要求连续 .我们的定理推广了近期的相应结果 . 相似文献
106.
In this paper, we devote ourselves to investigating a nonlocal problem involving singularity and asymptotically linear nonlinearities. By using the variational and perturbation methods, we obtain the existence of two positive solutions which improve the existing result in the literature. 相似文献
107.
Bruno de Andrade Carlos Lizama 《Journal of Mathematical Analysis and Applications》2011,382(2):761-771
In this paper, a class of nonlinear damped wave equations of the form αu?(t)+u″(t)=βAu(t)+γAu′(t)+f(t,u(t)), t?0, satisfying αβ<γ with prescribed initial conditions are studied. Some sufficient conditions are established for the existence and uniqueness of an asymptotically almost periodic solution. These results have significance in the study of vibrations of flexible structures possessing internal material damping. Finally, an example is presented to illustrate the feasibility and effectiveness of the results. 相似文献
108.
109.
ZeQingLIU ShinMinKANG 《数学学报(英文版)》2004,20(6):1009-1018
A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and hniagbosor (2000), Rhoades (1994) and Schu (1991). 相似文献
110.
In this paper, we investigate a class of stochastic functional differential equations of the form
dx(t)=(Ax(t)+F(t,x(t),xt))dt+G(t,x(t),xt)°dW(t). 相似文献