تقارب النقاط السرجية لدوال محدبة – مقعرة بالنسبة إلى مسافة - هاوسدورف
Abstract
الهدف من هذا البحث هو دراسة وتعميم بعض النتائج المتعلقة بـ - الحلول لمسائل بمتحول واحد (محدبة) إلى - الحلول لمسائل بمتحولين ( محدبة-مقعرة). إذ نعرف مسافة - هاوسدورف على صفوف الدوال المحدبة-المقعرة كما نعرف مسافة - هاوسدورف على صفوف دوال ليست بالضرورة
محدبة-مقعرة. ومن أجل المتتالية ندرس تقارب هذه المتتالية بدلالة تقارب المقاطع الموافقة لها، ثم نبرهن أن متقاربة نحو بالنسبة إلى مسافة - هاوسدورف إذا وفقط إذا كانت متتالية المجموعات متقاربة نحو المجموعة بالنسبة إلى مسافة - هاوسدورف . ونحصل على نتائج مشابهة تتعلق - التفاضلات الجزئية لدوال محدبة-مقعرة ومغلقة معرفة على فضاءات باناخ .
التصنيف الرياضي لهذا الموضوع AMS الأول : 46B20 الثاني : 49J45 .
The aim of this paper is to study and generalize some results concerned with the - solutions of one variable (convex) problems to the - solutions bivriables
(convex-concave) problems. We define the - Housdorff distanceon the classes to convex-concave functions and the - Housdorff distance on the classes not necessary convex-concave functions. For the sequence ; We study the convergence of this sequence in terms of level sets convergence, and we show that the sequence is - Housdorff distance to if and only if for each the sequence of sets is - Housdorff distance convergent to . An analogous result holds for - Subdifferential of convex-concave closed functions defined on a Banach space.
AMS Subject Numbers : Primary : 46B20
Secondary : 49J45.
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