• Title/Summary/Keyword: uniformly L-Lipschitzian mapping

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STRONG CONVERGENCE THEOREM FOR UNIFORMLY L-LIPSCHITZIAN MAPPINGS IN BANACH SPACES

  • Qin, Xiaolong;Kang, Shin Min;Shang, Meijuan
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.3
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    • pp.293-299
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    • 2008
  • In this paper, we prove strong convergence theorems for a finite family of uniformly L-Lipschitzian mappings by a cyclic iterative algorithm in the framework of Banach spaces. Our results improve and extend the recent ones announced by many others.

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THE CONVERGENCE THEOREMS FOR COMMON FIXED POINTS OF UNIFORMLY L-LIPSCHITZIAN ASYMPTOTICALLY Φ-PSEUDOCONTRACTIVE MAPPINGS

  • Xue, Zhiqun
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.2
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    • pp.295-305
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    • 2010
  • In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Finally, we obtain the convergence theorems of Ishikawa iterative sequence and the modified Ishikawa iterative process with errors.

ON ASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS IN ARBITRARY BANACH SPACES

  • Rafiq, Arif;Lee, Byung Soo
    • East Asian mathematical journal
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    • v.28 no.5
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    • pp.569-578
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    • 2012
  • In this paper, the necessary and sufficient conditions for the strong convergence of a modified Mann iteration process to a fixed point of an asymptotically demicontractive mapping in real Banach spaces are considered. Presented results improve and extend the results of Igbokwe [3], Liu [4], Moore and Nnoli [6] and Osilike [7].

A NEW APPROXIMATION SCHEME FOR FIXED POINTSOF ASYMPTOTICALLY ø-HEMICONTRACTIVE MAPPINGS

  • Kim, Seung-Hyun;Lee, Byung-Soo
    • Communications of the Korean Mathematical Society
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    • v.27 no.1
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    • pp.167-174
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    • 2012
  • In this paper, we introduce an asymptotically $\phi$-hemicontractive mapping with a $\phi$-normalized duality mapping and obtain some strongly convergent result of a kind of multi-step iteration schemes for asymptotically $\phi$-hemicontractive mappings.

Approximating Common Fixed Points of One-step Iterative Scheme with Error for Asymptotically Quasi-nonexpansive Type Nonself-Mappings

  • Puturong, Narongrit
    • Kyungpook Mathematical Journal
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    • v.49 no.4
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    • pp.667-674
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    • 2009
  • In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically non-expansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.