دراسة المشتقات فوق البيانية في فضاءات منظمة بالنسبة لتبولوجيا سلايس
Abstract
إن مفهوم المشتقات فوق البيانية, عرفها ودرسها الرياضي روكافولار [18] في فضاءات منتهية البعد مستخدما مفهوم التقارب فوق البيان ثم درسها كومنيتي [11] في فضاءات باناخ انعكاسية باستخدام مفهوم تقارب موسكو فوق البيان. الهدف من هذا البحث هو دراسة بعض هذه النتائج وتعميمها إلى فضاءات خطية منظمة غير منتهية البعد مستخدمين تقارباً جديداً يدعى تقارب سلايس فوق البيان. تسمح هذه النتائج في تحديد الشروط الأمثلية اللازمة والكافية لمسائل الأمثليات المحدبة العامة بالإضافة إلى أنَّها تملك تطبيقات هامة في العديد من النظريات الرياضية.
The epi-derivatives introduced and studied by Rockafellarin [18] finite-dimensional spaces in term to epi-convergence, are studied to convex functions in reflexive Banach spaces by cominite [11] in term to Mosco-epi-convergence. The purpose of this paper is to extend these results to general norm spaces, using a stronger convergence notion which is called Epigraphical Slice Convergence. Necessary and sufficient conditions are derived for general convex optimization. Moreover, this type of results has found application in numerous situations.
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