Banach空间中渐近非扩张映射的广义粘性隐式双中点法则

王元恒, 李参参

数学学报 ›› 2021, Vol. 64 ›› Issue (4) : 601-612.

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PDF(413 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (4) : 601-612. DOI: 10.12386/A2021sxxb0052
论文

Banach空间中渐近非扩张映射的广义粘性隐式双中点法则

    王元恒, 李参参
作者信息 +

The Generalized Viscosity Implicit Double Midpoint Rule for Asymptotically Non-expansive Mappings in Banach Spaces

    Yuan Heng WANG, Can Can LI
Author information +
文章历史 +

摘要

本文给出了实Banach空间中,渐近非扩张映射不动点的广义隐式双中点法则的粘性方法.在适当的参数条件下,证明了该算法生成的序列的强收敛定理.本文的结果推广和改进了其他作者的主要结果.

Abstract

We study viscosity method for the general implicit double midpoint rule for finding the fixed points of asymptotically non-expansive mappings in real Banach spaces. Under suitable conditions imposed on the parameters, some strong convergence theorems of the sequence generated by the algorithm are proved. The results presented in this article extend and improve the main results of other authors.

关键词

Banach空间 / 渐近非扩张映射 / 广义粘性隐式双中点法则 / 强收敛

Key words

Banach space / asymptotically non-expansive mapping / generalized viscosity implicit double midpoint rule / strong convergence

引用本文

导出引用
王元恒, 李参参. Banach空间中渐近非扩张映射的广义粘性隐式双中点法则. 数学学报, 2021, 64(4): 601-612 https://doi.org/10.12386/A2021sxxb0052
Yuan Heng WANG, Can Can LI. The Generalized Viscosity Implicit Double Midpoint Rule for Asymptotically Non-expansive Mappings in Banach Spaces. Acta Mathematica Sinica, Chinese Series, 2021, 64(4): 601-612 https://doi.org/10.12386/A2021sxxb0052

参考文献

[1] Bader G., Deuflhard P., A semi-implicit mid-point rule for stiff systems of ordinary differential equations, Numer. Math., 1983, 41:373-398.
[2] Cai G., Viscosity iterative methods for new variational inequality problems and fixed point problems in Hilbert spaces, Acta Math. Sin. Chin. Ser., 2019, 62(5):765-776.
[3] Cai G., Bu S. Q., Strong convergence theorems of a modified Mann iterative method for non-expansive mapping in Banach spaces (in Chinese), Acta Math. Sci. Ser. A, 2014, 34(1):1-8.
[4] Cai G., Shehu Y., Iyiola O. S., Modified viscosity implicit rules for non-expansive mappings in Hilbert spaces, J. Fixed Point Theory Appl., 2017, 19(4):2831-2846.
[5] Dhakal S., Sintunavarat W., The viscosity method for the implicit double midpoint rule with numerical results and its applications, Comput. Appl. Math., 2019, 38(2):1-18.
[6] Iiduka H., Takahashi W., Toyoda M., Approximation of solutions of variational inequalities for monotone mappings, Pan. Math. J., 2004, 14:49-61.
[7] Ke Y. F., Ma C. F., The generalized viscosity implicit rules of non-expansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015, 190:1-21.
[8] Luo P., Cai G., Shehu Y., The viscosity iterative algorithms for the implicit midpoint rule of non-expansive mappings in uniformly smooth Banach spaces, J. Inequal. Appl., 2017, 154:1-12.
[9] Liu C., Liu L. S., Strong convergence of modified Ishikawa iterative algorithm for non-expansive mappings with errors (in Chinese), Acta Math. Sin. Chin. Ser., 2016, 59(4):545-560.
[10] Lim T. C., Xu H. K., Fixed point theorems for asymptotically non-expansive mappings, Nonlinear Anal., 1994, 22:1345-1355.
[11] Pan C. J., Wang Y. H., Generalized viscosity implicit iterative process for asymptotically non-expansive mappings in Banach spaces, Mathematics, 2019, 7(5):1-13.
[12] Pan C. J., Wang Y. H., Viscosity approximation methods for a general variational inequality system and fixed point problems in Banach spaces, Symmetry Basel, 2020, 12(1):1-15.
[13] Somalia S., Implicit midpoint rule to the nonlinear degenerate boundary value problems, Int. J. Comput. Math., 2002, 79:327-332.
[14] Song Y., Chen R., Zho H., Viscosity approximation methods for non-expansive mapping sequences in Banach spaces, Nonlinear Anal., 2007, 66:1016-1024.
[15] Sunthrayuth P., Kumam P., Viscosity approximation methods base on generalized contraction mappings for a countable family of strict pseudo-contractions, a general system of variational inequalities and a generalized mixed equilibrium problem in Banach spaces, Math. Comput. Model, 2013, 58:1814-1828.
[16] Wu X., Zhao L., Viscosity approximation methods for multivalued non-expansive mappings, Mediterr. J. Math., 2016, 13:2645-2657.
[17] Xu H. K., Alghamdi M., Shahzad N., The viscosity technique for the implicit midpoint rule of non-expansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015, 41:1-12.
[18] Yao R. H., Chen R. D., Zhou H. Y., Iterative algorithms for fixed points of non-expansive mappings, Acta Math. Sin. Chin. Ser., 2007, 50(1):139-144
[19] Yao Y. H., Shahzad N., Liou Y. C., Modified semi-implicit midpoint rule for non-expansive mappings, Fixed Point Theory Appl., 2015, 166:1-15.
[20] Zhang H. C., Qu Y. H., Su Y. F., The generalized viscosity implicit midpoint rule for non-expansive Mappings in Banach Space, Mathematics, 2019, No.512, 16pp.
[21] Zeng L. C., Weak convergence theorems for non-expansive mapping in uniformly convex Banach spaces (in Chinese), Acta Math. Sin. Sci. Ser. A, 2002, 22(3):336-341.

基金

国家自然科学基金资助项目(11671365);浙江省自然科学基金资助项目(Y6100696)

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