Banach空间中Ishikawa迭代收敛定理

Convergence Theorems of Ishikawa Iteration in Banach Space

在Banach空间中,给出了平均非扩张映射‖Tx-Ty‖≤a‖x-y‖+b‖x-Ty‖的Ishikawa迭代收敛的充要条件,所得结果改进和推广了平均非扩张映射的Ishikawa迭代收敛的性质.

Abstract：The iterative approximation problems of fixed points are studied for mean nonexpansive mapping （｜｜Tx-Ty｜｜≤a｜｜x-y｜｜＋b｜｜x-Ty｜｜ ） in Sanach spaces. Some necessary and sufficient conditions are given for Ishikawa iterative sequence associated with mean nonexpansive mapping converge to fixed points. These results improve and extend the properties of Ishikawa iterative sequence associated with the mean nonexpansive mapping converge to fixed points