中文摘要：

目的是在Banach空间中引入并研究一类广义一致伪Lipschitz映象，举例说明这种映象的广泛性，并在一定条件下，证明了一族广义一致伪Lipschitz映象公共不动点的带误差的多步迭代序列收敛的充分必要条件，从而改进与推广了一些已知的结果．获得的收敛准则丰富了非线性算子不动点的迭代逼近理论．

英文摘要：

The purpose of this paper is to introduce and study a new class of generalized uniform quasi-Lipschitz mappings in Banach spaces and give an example to illustrate the universality of this kind of mapping. The sufficient and necessary condition for the multi-step iterative sequences with errors to converge strongly to a common fixed point for a finite family of generalized uniform quasi-Lipschitz mappings is proved under certain conditions, which improve and extend some recent results. We obtain the convergence criterion to enrich the iterative approximation theory of fixed point for nonlinear operators.