具一致广义Lipschitz连续算子的带误差的多步迭代间的收敛等价性

研究了一致光滑Banach空间中具一致广义Lipschitz连续的逐次渐近Φ-强伪压缩型算子的具误差的修正Mann迭代和具误差的修正多步Noor迭代间的收敛等价性问题,所得结果是对2007年Zhenyu Huang在一致光滑Banach空间中所建立的逼近具有有界值域的逐次Φ-强伪压缩算子的不动点具误差的修正Mann迭代和具误差的修正Ishikawa迭代两者的收敛是等价的这一结论更本质的和更一般的推广,所用的方法不全同于ZhenyuHuang所使用的方法,因此,从更一般的意义上肯定地回答了Rhoades和Soltuz于2003年所提出的猜想.

THE EQUIVALENCE BETWEEN THE CONVERGENCES OF MULTI-STEP ITERATIONS WITH ERRORS FOR UNIFORMLY GENERALIZED LIPSCHITZ CONTINUOUS OPERATORS

In this paper, the equivalence of the convergence of modified Mann iteration and multi-step Noor iteration with errors is invesgated for uniformly generalized Lipschitz continuous and successively asymptotically $Phi$-strongly pseudo-contractive type operators in uniformly smooth Banach spaces. In 2007, Zhenyu Huang showed the equivalence of the convergence criteria between modified Mann and Ishikawa iterations with errors for successively $Phi$-strongly pseudo-contractive operators with bounded range in uniformly smooth Banach spaces. The results obtained in this paper generalize the results of Huang in 2007. The results give an affirmative answer to the conjection raised by Rhoades and Soltuz in 2003.