锥度量空间中Picard迭代的T-稳定性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (2): 395-404.

锥度量空间中Picard迭代的T-稳定性

黄华平¹, 许绍元², 徐望斌¹

1. 湖北师范学院数学与统计学院湖北黄石 435002;
2. 韩山师范学院数学与统计系广东潮州 521041

收稿日期:2013-08-21 修回日期:2014-11-17 出版日期:2015-04-25 发布日期:2015-04-25
通讯作者: 许绍元 E-mail:xushaoyuan@126.com
基金资助:
韩山师范学院博士启动项目(QD20110920)资助

T-Stability of Picard's Iteration in Cone Metric Spaces

Huang Huaping¹, Xu Shaoyuan², Xu Wangbin¹

1. School of Mathematics and Statistics, Hubei Normal University, Hubei Huangshi 435002;
2. Department of Mathematics and Statistics, Hanshan Normal University, Guangdong Chaozhou 521041

Received:2013-08-21 Revised:2014-11-17 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

摘要：

研究了锥度量空间中关于压缩映射和扩张映射的Picard 迭代的T-稳定性, 并且列举了一些例子验证了其结论. 同时通过应用这些结论, 获得了一类常见的带有边值条件的微分方程的正解公式.

关键词: T-稳定性, 锥度量空间, 压缩映射, 扩张映射, 不动点

Abstract:

In this paper we investigate the T-stability of fixed point Picard's iteration procedures for contractive mappings and expansive mappings, respectively. We illustrate our conclusions for some examples. Furthermore, we use our results to obtain the unique positive solution for an ordinary differential equation with boundary conditions.

Key words: T-Stability, Cone metric space, Contractive mapping, Expansive mapping, Fixed point

中图分类号:

O177.91

黄华平, 许绍元, 徐望斌. 锥度量空间中Picard迭代的T-稳定性[J]. 数学物理学报, 2015, 35(2): 395-404.

Huang Huaping, Xu Shaoyuan, Xu Wangbin. T-Stability of Picard's Iteration in Cone Metric Spaces[J]. Acta mathematica scientia,Series A, 2015, 35(2): 395-404.

参考文献

[1] Aage C T, Salunke J N. Some fixed point theorems for expansion onto mappings on cone metric spaces. Acta Mathematica Sinica, 2011, 27(6): 1101-1106

[2] Asadi M, Soleimani H, Vaezpour S M, Rhoades B E. On T-stability of Picard iteration in cone metric spaces. Fixed Point Theory and Applications, 2009, Article ID 751090, 6 pages

[3] Han Y, Xu S Y. Some new theorems of expanding mappings without continuity in cone metric spaces. Fixed Point Theory and Applications, 2013, 1(3): 1-9

[4] Harder A M, Hicks T L. Stability results for fixed point iteration procedures. Mathematica Japonica, 1988, 33(5): 693-706

[5] Huang L G, Zhang X. Cone metric spaces and fixed point theorems of contractive mappings. Journal of Mathematical Analysis and Applications, 2007, 332(2): 1468-1476

[6] Jankovi? S, Kadelburg Z, Radenovi? S. On cone metric spaces: a survey. Nonlinear Analysis, 2011, 74: 2591-2601

[7] Kadelburg Z, Murthy P P, Radenovi? S. Common fixed points for expansive mappings in cone metric spaces. Intertional Journal of Mathematical Analysis, 2011, 5(27): 1309-1319

[8] Osilike O M. Stability results for fixed point iteration procedures. Journal of the Nigerian Mathematical Society, 1995, 14: 17-29

[9] Qing Y, Rhoades B E. T-stability of Picard iteration in metric spaces. Fixed Point Theory and Applications, 2008, Article ID 418971, 4 pages

[10] Rezapour Sh, Hamlbarani R. Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings". Journal of Mathematical Analysis and Applications, 2008, 345: 719-724

[11] Rhoades B E. Fixed point theorems and stability results for fixed point iteration procedures. Indian Journal of Pure and Applied Mathematics, 1990, 12(1): 1-9

[12] Shatanawi W. On w-compatible mappings and common coupled coincidence point in cone metric spaces. Applied Mathematics Letters, 2012, 25: 925-931

[13] Shatanawi W, Awawdeh F. Some fixed and coincidence point theorems for expansive maps in cone metric spaces. Fixed Point Theory and Applications, 2012, 1(19): 1-19

[14] Song G X, Sun X Y, Zhao Y A, Wang G T. New common fixed point theorems for maps on cone metric spaces. Applied Mathematics Letters, 2010, 23: 1033-1037

[15] Wang J Y. The subrepresentation theorems of the conjugate cones of real locally p-convex spaces l^p and L^p(μ) (0

30A(6): 1629-1639

[16] Zhang X. Fixed point theorem of generalized operator quasi-contractive mapping in cone metric space. African Mathematics, 2014, 25: 135-146