دراسة النقطة الثابتة في الفضاء اللاأرخميدي
Abstract
الهدف من هذا العمل هو دراسة بعض الدوال المستمرة والمعرفة على فضاءات حقيقية والتي تملك نقطة ثابتة، ثم نقل هذه الدوال ودراستها على فضاءات معرفة على حقول لا أرخميدية
((Non-Archimedean vector spaces))، وبيان هل مثل هذه الدوال موجودة، أو موجودة ضمن شروط محددة، و دراسة النقطة الثابتة لهذه الدوال. وقد أثبتنا انه إذا كان الحقل K مقيما لا أرخميدياً , وكان معياريا يحقق الشرطين و، عندئذ لا يوجد دالي محدود وغير مبتذل في الفضاء المعير . أما إذا كان فضاء لا ارخميديا كروياً تاماً ومنظماً، وكان التطبيق تطبيقا مقلصا فإن يملك نقطة ثابتة.
The purpose of this article is to study the behavior of some functions of spaces over field K (Real or Complex). These functions must be continuous, realize specific conditions and have fixed point. We will then study the existence of those functions after defining the above spaces over Non-Archimedean field. Afterwards, we will study the fixed its points. We prove that, if K is a non-Archimedean valued field and a modular satisfying the conditions D2 and B2.
There exists no nontrivial modular bounded linear functional in the modular space X. We also show, if be a Non-Archimedean spherically complete formed space, and is contractive mapping then has a unique fixed point.
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