Banach空间中一类新α-β-非扩张映射的迭代收敛问题

Iterative Convergence of a Class of New α-β-Non-expansive Mappings in Banach Space

定义了一类新的α-β-非扩张映射,在一定条件下,证明了这类非扩张映射修改的Ishikawa迭代序列收敛于它的不动点;然后,给出了修改的Ishikawa迭代序列强收敛到这类非扩张映射的不动点的一个充要条件;最后证明了在一定条件下,如果F(T)非空,则‖Tnxn-xn‖→0(n→∞).

This paper defines a class of new a-fl-non-expansive mappings, under certain condition, proves that the modified Ishikawa iteration sequence of this class of non-expansive mappings converges to its fixed point, then gives a sufficient and necessary condition for the modified Ishikawa iteration sequence to strongly converge to the fixed point of this class of non-expansive mappings, and finally proves that under certain condition, if F（T） is not empty, then ｜｜ Tnxn-xn｜｜→0（n→∞）.