استخدام التقسيم النظامي للسيمبلكس النوني القياسي في إثبات مبرهنة بروور للنقطة الثابتة

Authors

  • محمود باكير

Abstract

تعد مبرهنة بْرووَر للنقطة الثابتة من المبرهنات الهامة في الأدبيات الرياضية، وهي تعميم لمبرهنة القيمة المتوسطة للتوابع المستمرة، ولها العديد من الإثباتات المعروفة. نثبت أولاً أنه إذا كان   السيمبلكس القياسي في وكان لدينا تابع مستمر من  إلى نفسه، فإن لهذا التابع نقطة ثابتة واحدة على الأقل، وذلك اعتماداً على التقسيم النظامي للسيمبلكس النوني القياسي. ثم نثبت أنه أية مجموعة متراصة ومحدبة في  فإنها تتمتع بخاصة النقطة الثابتة.

The Brouwer Fixed Point Theorem is one of the very well–known theorems in mathematics. It is a generalization of the Intermediate-Value Theorem. It also has many proofs. First, we prove that if  is a standard simplex in , and we have a continuous function from  to itself, then, by using the standard division of the standard n–simplex, this function has at least one fixed point. Then, we prove that any compact convex subset in has the property of the fixed point.

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Published

2018-12-05

How to Cite

1.
باكير م. استخدام التقسيم النظامي للسيمبلكس النوني القياسي في إثبات مبرهنة بروور للنقطة الثابتة. TUJ-BA [Internet]. 2018Dec.5 [cited 2025Apr.14];30(2). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/5051

Issue

Vol. 30 No. 2 (2008): العلوم الأساسية

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Articles

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