• Title/Summary/Keyword: modified Ishikawa iteration processes

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ITERATION PROCESSES OF ASYMPTOTICALLY PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

  • Park, Jong-Yeoul;Jeong, Jae-Ug
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.611-622
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    • 2001
  • Some convergence theorems of modified Ishikawa and Mann iteration processes with errors for asymptotically pseudo-contractive and asymptotically nonexpansive mappings in Banach spaces are obtained. The results presented in this paper improve and extend the corresponding results in Liu [7] and Schu [10].

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Strong Convergence of Modified Iteration Processes for Relatively Nonexpansive Mappings

  • Kim, Tae-Hwa;Lee, Hwa-Jung
    • Kyungpook Mathematical Journal
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    • v.48 no.4
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    • pp.685-703
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    • 2008
  • Motivated and inspired by ideas due to Matsushida and Takahashi [J. Approx. Theory 134(2005), 257-266] and Martinez-Yanes and Xu [Nonlinear Anal. 64(2006), 2400-2411], we prove some strong convergence theorems of modified iteration processes for a pair (or finite family) of relatively nonexpansive mappings in Banach spaces, which improve and extend the corresponding results of Matsushida and Takahashi and Martinez-Yanes and Xu in Banach and Hilbert spaces, repectively.

REMARKS ON APPROXIMATION OF FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS

  • Kim, Tae-Hwa;Kim, Eun-Suk
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.461-475
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    • 2000
  • In the present paper, we first give some examples of self-mappings which are asymptoticaly nonexpansive in the intermediate, not strictly hemicontractive, but satisfy the property (H). It is then shown that the modified Mann and Ishikawa iteration processes defined by $x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^nx_n\ and\ x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^n[(1-\beta_n)x_n+\beta_nT^nx_n]$,respectively, converges strongly to the unique fixed point of such a self-mapping in general Banach spaces.

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