渐近非扩张型映射的不动点迭代和Δ-收敛定理

左占飞

数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 387-394.

PDF(427 KB)
中国科学院数学与系统科学研究院期刊网
PDF(427 KB)
数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 387-394. DOI: 10.12386/A2014sxxb0038
论文

渐近非扩张型映射的不动点迭代和Δ-收敛定理

    左占飞
作者信息 +

Fixed-Point Iterations and Δ-Convergence Theorem for Mappings of Asymptotically Nonexpansive Type

    Zhan Fei ZUO
Author information +
文章历史 +

摘要

研究了一致凸双曲度量空间中渐近非扩张型映射的三步迭代，这种迭代包括了Ishikawa型迭代和Krasnoselski-Mann迭代作为特例.作为应用还得到了迭代算法在CAT（0）空间中的Δ-收敛定理，得到的结论推广并加强了以前的许多已知结果.

Abstract

We analyze a three-step iterative scheme for mappings of asymptotically nonexpansive type in uniformly convex hyperbolic spaces. The new iterative scheme includes Ishikawa-type and Krasnoselski-Mann iteration as special cases. As an application, we obtain a Δ-convergence theorem of the three-step iterative scheme for mappings of asymptotically nonexpansive type in CAT(0) spaces. The results obtained in this paper represent an extension as well as refinement of previous known results.

关键词

三步迭代 / 渐近非扩张型映射 / 一致凸双曲度量空间 / Δ-收敛定理 / CAT(0)空间

Key words

three-step iterations / asymptotically nonexpansive type mapping / uniformly convex hyperbolic spaces / Δ-convergence theorem / CAT(0) spaces

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用
左占飞. 渐近非扩张型映射的不动点迭代和Δ-收敛定理. 数学学报, 2014, 57(2): 387-394 https://doi.org/10.12386/A2014sxxb0038
Zhan Fei ZUO. Fixed-Point Iterations and Δ-Convergence Theorem for Mappings of Asymptotically Nonexpansive Type. Acta Mathematica Sinica, Chinese Series, 2014, 57(2): 387-394 https://doi.org/10.12386/A2014sxxb0038

参考文献

[1] Bridson M., Haefliger A., Metric Spaces of Non-positive Curvature, Grundlehren der Mathematischen Wissenschaften, Vol. 319, Springer, Berlin, 1999.
[2] Bruck R. E., Kuczumow T., Reich S., Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloqium Math., 1993, LXV: 169-179.
[3] Busemann H., Spaces with non-positive curvature, Acta Math., 1948, 80: 259-310.
[4] Dhompongsa S., Payanak B., On Δ-converges theorems in CAT(0) spaces, Comput. Math. Appl., 2008, 56: 2572-2579.
[5] Geobel K., KirkW. A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 1972, 35: 171-174.
[6] Goebel K., Reich S., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, In: Monographs Textbooks in Pure and Applied Mathematices, Marcel Dekker, Inc., New York 1984.
[7] Kaczor W., Walczuk J., A mean ergodic theorem for mappings which are asymptotically nonexpansive in the intermediate sense, Nonlinear Anal. Theory Methods Appl., 2001, 47: 2731-2742.
[8] Khamsi M. A., Khan A. R., Inequalities in metric spaces with applications, Nonlinear Anal. Theory Methods Appl., 2011, 74: 4036-4045.
[9] Kirk W. A., Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive types, Israel J. Math., 1974, 17: 339-346.
[10] Kirk W. A., Panyanak B., A concept of convergence in geodesic spaces, Nonlinear Anal. Theory Methods Appl., 2008, 68: 3689-3696.
[11] Kohlenbach U., Leustean L., Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces, J. Eur. Math. Soc., 2010, 12: 71-92.
[12] Laokul T., Panyanak B., Approximating fixed points of nonexpansive mappings in CAT(0) spaces, Int. J. Math. Anal., 2009, 27: 1305-1315.
[13] Lim T. C., Remarks on some fixed point theorems, Proc. Amer. Math. Soc., 1976, 60: 179-182.
[14] Menger K., Untersuchungen über allgemeine metrik, Math. Ann., 1928, 100: 75-163.
[15] Nanjaras B., Panyanak B., Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl., 2010, Article ID 268780.
[16] Rhoades B. E., Soltuz S. M., The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps, J. Math. Anal. Appl., 2004, 289: 266-278.
[17] Tits F. J., Groupes réducifs sur un corps local, Institut des Hautes Ėtudes Scientifiques, Publications Mathématiques de l'IH ĖS, 1972, 41: 5-251.
[18] Xu B. L., Noor M. A., Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 2002, 267: 444-453.
[19] Xu H. K., Existence and convergence for fixed points of mappings of asymptotically nonexpansive type, Nonlinear Anal. Theory Methods Appl., 1991, 16: 1139-1146.

基金

重庆市教委科学技术研究项目资助（KJ131104）
PDF(427 KB)

241

Accesses

0

Citation

Detail
段落导航
相关文章

/

〈 〉