双曲空间中几乎渐近非扩张型映象不动点的收敛性定理

Convergence theorems of fixed points for nearly asymptotically nonexpansive mappings in hyperbolic spaces

摘要: 介绍了一个改进的逼近几乎Lipschitzian连续映象不动点的SP-迭代方法,在双曲空间中建立了关于几乎渐近非扩张映象不动点的Δ-收敛性定理,并在映象T具有半紧性的条件下证明了相应的SP-迭代序列强收敛到映象T的某个不动点.

Abstract: A modified SP-iteration process is introduced to approximate a fixed point of a nearly Lipschitzian mapping.The Δ-convergence theorem of a nearly asymptotically nonexpansive mapping is established in hyperboloic spaces.Moreover,the strong convergence theorems of the SP-iterative sequences are proved under the conditions of demicompactness defined on mapping T.