【作者】 邢林芳；

【导师】 陈汝栋；

【作者基本信息】 天津工业大学 ， 应用数学， 2008， 硕士

【摘要】 在本文中,首先在Hilbert空间H上研究了非扩张非自映象下的显式均值迭代过程,并得到了强收敛结果.这些结果推广和改进了文献Y.S.Song,R.D.Chen[Viscosity approximation methods for nonexpansive nonself-mappings,J.Math.Anal.Appl.321(2006)316-326],S.Matsushita,D.Kuroiwa[Strong convergence ofaveraging iterations of nonexpansive mappings,J.Math.Anal.Appl.294(2004)206-214]相应的结果.接着,研究了Hilbert空间H的非空闭凸子集C上的渐进非扩张非自映像,利用CQ方法构造迭代序列{x_n),{y_n),并得到了强收敛结果.该结果推广和改进了文献T.H.Kim,H.-K.Xu[Strong convergence of modified Mann iterationsfor asympototically nonexpansive mappings and semigroups,Nonlinear Anal.64(2006)1140-1152]相应的结果.接着,在q—一致光滑的Banach空间上,利用向阳非扩张映象特点构造迭代算法,来逼近变分不等式组的解的问题.该结果推广和改进了R.U.Verma[Generalconvergnece analysis for two-step projection methods and applications to variationalproblems,Appl.Math.Lett.18(2005)1286-1292]相应的结果.最后,初步尝试利用计算机对相应算法进行算法实现即比较了Picard迭代序列,Mann迭代序列及Ishikawa迭代序列的收敛速度的问题,具有一定的理论意义和实际意义.更多还原

【Abstract】 In this paper,firstly in Hilbert spaces H,we consider the explicit averaging iterations of nonexpansive nonself mappings,and get strong convergent results. The results presented extend and improve the corresponding ones of Y.S. Song and R.D.Chen[Viscosity approximation methods for nonexpansive nonselfmappings, J.Math.Anal.Appl.321(2006)316-326]and S.Matsushita,D.Kuroiwa [Strong convergence of averaging iterations of nonexpansive mappings,J.Math. Anal.Appl.294(2004)206-214].Then,we consider another iteration,that is,the iteration of asymptotically nonexpansive mappings of the nonempty closed convex subset C to Hilbert spaces H.We use CQ methods to construct the iterations {x_n},{y_n},and get strong convergent results.The results presented extend and improve the corresponding ones of T.H.Kim,H.-K.Xu[,Strong convergence of modified Mann iterations for asympototically nonexpansive mappings and semigroups,Nonlinear Anal. 64(2006)1140-1152].Next,in q- uniformly Banach spaces,we construct iteration algorithm through sunny nonexpansive mappings to approach the solutions of a system of two nonlinear variational inequalities problem.The results presented extend and improve the corresponding ones of R.U.Verma[General convergnece analysis for two-step projection methods and applications to variational problems, Appl.Math.Lett.18(2005)1286-1292].At last,we preliminarily attempt to use computer and compare the speed of the common iterative sequences such as Picard iterative sequence,Mann iterative sequence and Ishikawa iterative sequence.The result has certain theory significance and the practical significance.更多还原