Journal article
Fixed point theorems for noncommutative functions
Journal of mathematical analysis and applications, v 401(1), pp 436-446
01 May 2013
Featured in Collection : UN Sustainable Development Goals @ Drexel
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. (C) 2012 Elsevier Inc. All rights reserved.
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Details
- Title
- Fixed point theorems for noncommutative functions
- Creators
- Gulnara Abduvalieva - Drexel UniversityDmitry S. Kaliuzhnyi-Verbovetskyi - Drexel University
- Publication Details
- Journal of mathematical analysis and applications, v 401(1), pp 436-446
- Publisher
- Elsevier
- Number of pages
- 11
- Grant note
- 2010432 / US-Israel BSF; US-Israel Binational Science Foundation DMS 0901628 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000314739000045
- Scopus ID
- 2-s2.0-84872898562
- Other Identifier
- 991019168973904721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied