Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (1): 31-37.

• Articles • Previous Articles     Next Articles

Approximating Fixed Points of Asymptotically Nonexpansive Mappings in Banach Spaces

 CENG Liu-Chuan   

  • Online:2003-02-25 Published:2003-02-25
  • Supported by:

    国家自然科学基金资助项目(19801023); 高等学校优秀青年教师教学和科研奖励基金资助项目

Abstract:

Let E be a uniformly convex Banach space,  $C$ be a nonempty closed convexsubset of $E$, and $T:C→C$  be an asymptotically nonexpansive mapping with fixed points. It is shown that under some suitable conditions, the sequence ${x\-n}$ defined by the modified Ishikawa iteration process: $$x\-\{n+1\}=t\-nT\+n(s\-nT\+nx\-n+(1-s\-n)x\-n)+(1-t\-n)x\-n,$$converges weakly to a fixed point of $T$, where ${t\-n}$ and ${s\-n}$ aresequences in 

0,1
with some restrictions.

Key words: Fixed point, Asymptotically nonexpansive mapping, Modified Ishikawa iteration process, Uniformly convex Banach space

CLC Number: 

  • 47H09
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