کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4616983 1339364 2013 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Fixed point theorems for noncommutative functions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Fixed point theorems for noncommutative functions
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 401, Issue 1, 1 May 2013, Pages 436–446
نویسندگان
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