一般Banach空间中渐近非扩张型半群的不动点定理

Abstract

Abstract:

This paper is first devoted to proving two existence theorems of fixed points for asymptotically nonexpansive type semigroups in general Banach spaces. Based on these results, a strong convergence theorem of Mann's type sequences for the asymptotically nonexpansive type semigroups is given. The main results extend the
results of Suzuki and Takahashi to the case of the non-Lipschitzian semigroups.

Key words: Fixed , point, Asymptotically nonexpansive type semigroup, Mann's type sequences, Strong convergence theorem

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SHU Lan-Ping, LI Gang. Fixed Point |Theorems for Asymptotically Nonexpansive Type Semigroups in General Banach Spaces[J].Acta mathematica scientia,Series A, 2009, 29(2): 290-296.

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References

[1] Bruck R E, Kuczumow T, Reich S. Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property. Colloq Math, 1993, 65(2): 169--179

[2] Kirk W A, Torrejon R. Asymptotically nonexpansive semigroup in Banach space. Nonlinear Analysis TMA, 1979, 3(1): 111--121

[3] Suzuki T, Takahashi W. Strong convergence of Mann's type sequences for one-parameter nonexpansive semigroups in general Banach spaces. J Nonlinear Convex Anal, 2004, 5(2): 209--216

[4] Suzuki T. Strong convergence theorem to common fixed points of two nonexpansive mappings in general Banach spaces. J Nonlinear Convex Anal, 2002, 3(3): 381--391

[5] Takahashi W. Nonlinear Functional Analysis. Yokohama: Yokohama Publishers, 2000

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Fixed Point |Theorems for Asymptotically Nonexpansive Type Semigroups in General Banach Spaces

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