 ,(3.2)
且
  ,(3.3)
其中
根据(3.1),(3.2)及(3.3)式，得到
 (3.4)
定义一个实凸函数 对一切 且 及一切 ，有
 (3.5)
根据（3.1）及（3.5）式，得到
 (3.6)
 (3.7)
这里
将(3.6)，(3.7)代入(3.4)，有
这里
由于  所以
 即 强收敛于 的唯一不动点 ．
参考文献
[1]Zhang S. S.,Iterative approximation problem of fixed points for asymptotically nonexpansivemappings in Banach spaces, Acta Math. Appl. Sinica, 2001
[2]J. K. Kim, D. R. Sahu, Convergence theorem for fixed points ofnearly uniformly  Lipschitzianasymptotically generalized  hemicontractive mappings, Nonlinear analysis,2009
[3]C. E. Chidume andC. O. Chidume, Convergence theorem for zeros of generalized Lipschitze generalizedquasiaccretiveoperators, Proc. Amer. Math. Soc., 2006
[4]Tang Y. C.,Note onsome results for asymptotically pseudocontractive mappings and asymptoticallynonexpansive mappings
[5]Chang S. S., Someproblems and results in the study of nonlinear analysis, Norlinear Anal. TMA,1997
[6]Tan K. K., Xu H.K., Approximating fixed points of nonexpansive mappings by the Ishikawaiteration process, J. Math. Anal. Appl.,1993
[7]X.Weng, Fixedpoint iteration for local strictly pseudocontractive mapping, Proc. Amer. Math.Soc., 2001
[8]Chang S. S., Someresults for asymptotically pseudocontractive mappings and asymptotically nonexpansivemappings, Proc. Amer. Math. Soc., 2001
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