【作者】 李雪松；

【导师】 黄南京；

【作者基本信息】 四川大学 ， 应用数学， 2006， 硕士

【摘要】 本文在Banach空间中分别研究了几类映象的显式与隐式迭代序列的强、弱收敛性在第一章中,我们对Banach空间中有界凸集上的一致拟Lipschitzian映象S,T证明了带误差的Ishikawa迭代序列收敛到其公共不动点的一个充要条件,其中S,T不必连续。在第二章中,对于Banach空间中的一簇中间意义下的渐近拟非扩张映象的隐式迭代序列的收敛性,我们给出了一个充要条件,并在一致凸Banach空间中讨论了该隐式迭代序列的收敛性。在第三章中,在一致凸Banach空间中,对于一簇非自渐近拟非扩张映象类构成的显式迭代序列,我们分别给出了一些适当的条件,并得出了一些强、弱收敛性结论。更多还原

【Abstract】 In this paper,we respectively study the strong and weak convergence for explicitand implicit iteration sequences of some mappings in Banach space.In Chapter 1, A sufficient and necessary condition is proved for Ishikawa itera-tive sequence of uniformly quasi-Lipschitzian mappings S,Twith errors to converge tofixed points, where S,T defined on a bounded convex set need not be continuous.In Chapter 2, We prove a sufficient and necessary condition for the implicit iter-ation sequence converges to a common fixed point of a finite family of asymptoticallyquasi-nonexpansive mappings in the intermediate sense in Banach spaces. We alsodiscuss the convergence of the implicit iteration sequence in uniformly convex Banachspaces.In Chapter 3, For the explicit iteration sequence constructed by a finite family ofnon-self asymptotically quasi-nonexpansive type,we obtain some conclusions of strongand weak convergence,respectively under some suitable conditions.更多还原