دراسة المشتقات فوق البيانية من المرتبة الأولى للدوال المحدبة في فضاءات منظمة
Abstract
درس الرياضي روكافولار المشتقات فوق البيانية من المرتبة الأولى في فضاءات منتهية البعد مستخدماً مفهوم التقارب فوق البيان ومن ثم تمت دراستها من قبل دو في فضاءات باناخ انعكاسية مستخدماً مفهوم التقارب لموسكو . أما عملنا فسيكون تعميم هذه المشتقات إلى فضاءات منظمة عامة باستخدام مفهوم جديد للتقارب يسمى تقارب سلايس ويتطابق مع مفهوم التقارب فوق البيان إذا كان الفضاء منتهي البعد , ويتطابق مع تقارب موسكو إذا كان الفضاء انعكاسياً ويعود هذا المفهوم إلى الرياضي بيير.
Rockafeller introduced the epi- derivatives in terms of epi-convergence in finit dimensional space , and Do studied these results in terms of Mosco- convergence in reflexive Banach space.
The aim of this paper is to extend these setting to general normal spaces, using a stronger convergence notion called Epigraphical Slice Convergence introduced by Beer. It coincides with the epi- convergence in finit dimensional space and coincides with Mosco-convergence in reflexive Banach space.
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