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- Title
On the stability of finding approximate fixed points by simplicial methods.
- Authors
Song, Qi-Qing; Yang, Hui; Yang, Guang-Hui; Zhong, Chong-Yi
- Abstract
This paper reports some new results in relation to simplicial algorithms considering continuities of approximate fixed point sets. The upper semi-continuity of a set-valued mapping of approximate fixed points using vector-valued simplicial methods is proved, and thus one obtains the existence of finite essential connected components in approximate fixed point sets by vector-valued labels; examples are given to show that this is very different from the property for integer-valued labeling simplicial methods. The existence of essential sets is also proved focusing on both perturbations of domains and functions.
- Subjects
FIXED point theory; SET-valued maps; VECTOR-valued measures; PERTURBATION theory; SIMPLEX algorithm
- Publication
Journal of Inequalities & Applications, 2016, Vol 2016, Issue 1, p1
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1186/s13660-016-1162-5