Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616983 | Journal of Mathematical Analysis and Applications | 2013 | 11 Pages |
Abstract
We establish a fixed point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions are stronger if such a mapping also respects matrix similarities, i.e., is a noncommutative function. As a special case, we prove the corresponding contractive mapping theorem which can be viewed as a new version of the Banach Fixed Point Theorem. This result is then applied to prove the existence and uniqueness of a solution of the initial value problem for ODEs in noncommutative spaces. As a by-product of the ideas developed in this paper, we establish a noncommutative version of the principle of nested closed sets.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Gulnara Abduvalieva, Dmitry S. Kaliuzhnyi-Verbovetskyi,