摘要:本文研究了解Banach空间中，非线性算子方程的带参数的修正型超Halley迭代族的局部收敛性问题，在算子的二阶导数满足Lipschitz条件下，建立了修正型超Halley迭代族的3阶局部收敛性。

关键词:非线性算子方程  修正型超Halley迭代族  3阶收敛性

Abstract: The convergence problems of the family of the deformed Super-Halley iterations with parameters for solving nonlinear operator equations in Banach spaces are studied. Under the assumption that the derivative of the operator satisfies the Lipschitz condition, the Local quadratic convergences of the family of the deformed Super-Halley iterations are established.

Keyword: Nonlinear operator equation    the family of the deformed Super-Halley iterations      the quadratic convergence