• 제목/요약/키워드: normalized duality mappings

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A CHARACTERIZATION OF THE GENERALIZED PROJECTION WITH THE GENERALIZED DUALITY MAPPING AND ITS APPLICATIONS

  • Han, Sang-Hyeon;Park, Sung-Ho
    • 대한수학회논문집
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    • 제27권2호
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    • pp.279-296
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    • 2012
  • In this paper, we define a generalized duality mapping, which is a generalization of the normalized duality mapping and using this, we extend the notion of a generalized projection and study their properties. Also we construct an approximating fixed point sequence using the generalized projection with the generalized duality mapping and prove its strong convergence.

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

  • Qin, Xiaolong;Kang, Shin Min;Shang, Meijuan
    • 충청수학회지
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    • 제21권3호
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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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STRONG CONVERGENCE OF MODIFIED ISHIKAWA ITERATION FOR TWO RELATIVELY NONEXPANSIVE MAPPINGS IN A BANACH SPACE

  • Liu, Ying;Wang, Xian;He, Zhen
    • East Asian mathematical journal
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    • 제25권1호
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    • pp.97-105
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    • 2009
  • In this paper, we prove a strong convergence theorem for a common fixed point of two relatively nonexpansive mappings in a Banach space by using the modified Ishikawa iteration method. Our results improved and extend the corresponding results announced by many others.

STRONG CONVERGENCE THEOREMS BY VISCOSITY APPROXIMATION METHODS FOR ACCRETIVE MAPPINGS AND NONEXPANSIVE MAPPINGS

  • Chang, Shih-Sen;Lee, H.W. Joseph;Chan, Chi Kin
    • Journal of applied mathematics & informatics
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    • 제27권1_2호
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    • pp.59-68
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    • 2009
  • In this paper we present an iterative scheme for finding a common element of the set of zero points of accretive mappings and the set of fixed points of nonexpansive mappings in Banach spaces. By using viscosity approximation methods and under suitable conditions, some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper improve and extend the corresponding results of Kim and Xu [Nonlinear Anal. TMA 61 (2005), 51-60], Xu [J. Math. Anal. Appl., 314 (2006), 631-643] and some others.

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ON THE STRONG CONVERGENCE THEOREMS FOR ASYMPTOTICALLY NONEXPANSIVE SEMIGROUPS IN BANACH SPACES

  • Chang, Shih-Sen;Zhao, Liang Cai;Wu, Ding Ping
    • Journal of applied mathematics & informatics
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    • 제27권1_2호
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    • pp.13-23
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    • 2009
  • Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are established. The results presented in this paper extend and improve some recent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133-2136; H. K. Xu. A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371-379; N. Shioji and W. Takahashi. Strong convergence theorems for continuous semigroups in Banach spaces, Math. Japonica. 1(1999)57-66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211(1997)71-83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87-99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157-163.]

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