دراسة المشتقات من المرتبة الثانية لدوال محدبة –مقعرة وفق مسافة ????-هاوسدورف
Abstract
تلعب المشتقات فوق البيانية من المرتبة الثانية دورا هاما في حل مسائل الأمثليات وتحديد شروط لها, وكان روكافولار أول من درس مشتقات الدوال المحدبة والمحدبة –المقعرة في فضاءات منتهية البعد ومن ثم تناولها العديد من الرياضيين . يهدف هذا البحث إلى دراسة وتعميم المشتقات فوق البيانية من المرتبة الثانية لدوال محدبة-مقعرة الى فضاءات باناخ وفضاءات منظمة باستخدام مفهوم مسافة -هاوسدورف والحصول على نتائج هامة تتعلق بالمشتقات فوق البيانية للدوال القرينة المحدبة ومشتقات الدوال القرينة المقعرة وكذلك بالمشتق البياني للمؤثرات التفاضلية الموافقة لها. The second –order epi derivatives play an important role in nonsmooth analysis and in statements of optimality conditions ,these notions introduced by Rockafellar for convex functions and convex−concave functions in finite dimensional spaces. It is purpose of this paper is to study and extend the epi-derivatives for convex – concave functions to general Banach spaces and normed spaces using -Hausdorff distance convergence, and obtain important results for the epi-derivative of parent convex functions , parent concave functions and proto-derivative of subdifferential operatorDownloads
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