系统科学与数学
繫統科學與數學
계통과학여수학
JOURNAL OF SYSTEMS SCIENCE AND MATHEMATICAL SCIENCES
2010年
3期
398-409
,共12页
一致广义Lipschitz连续算子%逐次渐近Φ-强伪压缩型算子
一緻廣義Lipschitz連續算子%逐次漸近Φ-彊偽壓縮型算子
일치엄의Lipschitz련속산자%축차점근Φ-강위압축형산자
Uniformly generalized Lipschitz continuous operator%successively asymptotically F-strongly pseudo-contractive type operator
研究了一致光滑Banach空间中具一致广义Lipschitz连续的逐次渐近江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-般的意义上肯定地回答了Rhoades和Soltuz于2003年所提出的猜想.
研究瞭一緻光滑Banach空間中具一緻廣義Lipschitz連續的逐次漸近江彊偽壓縮型算子的具誤差的脩正Mann迭代和具誤差的脩正多步Noor迭代間的收斂等價性問題,所得結果是對2007年zhenyu Huang在一緻光滑Banach空間中所建立的逼近具有有界值域的逐次Φ-彊偽壓縮算子的不動點具誤差的脩正Mann迭代和具誤差的脩正Ishikawa迭代兩者的收斂是等價的這一結論更本質的和更一般的推廣,所用的方法不全同于zhenyuHuang所使用的方法,因此,從更-般的意義上肯定地迴答瞭Rhoades和Soltuz于2003年所提齣的猜想.
연구료일치광활Banach공간중구일치엄의Lipschitz련속적축차점근강강위압축형산자적구오차적수정Mann질대화구오차적수정다보Noor질대간적수렴등개성문제,소득결과시대2007년zhenyu Huang재일치광활Banach공간중소건립적핍근구유유계치역적축차Φ-강위압축산자적불동점구오차적수정Mann질대화구오차적수정Ishikawa질대량자적수렴시등개적저일결론경본질적화경일반적추엄,소용적방법불전동우zhenyuHuang소사용적방법,인차,종경-반적의의상긍정지회답료Rhoades화Soltuz우2003년소제출적시상.
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 F-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 F-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.
