مجموعات تحول قيم بعض الداليات العقدية في فضاء كاراتيودوري المعمم
Abstract
يقدم هذا البحث طريقة معينة لتحديد مجموعات تحول قيم بعض الداليات الخطية في فضاء كاراتيودوري المعمم وهو فضاء التوابع التحليلية في قرص الواحدة التي تقبل التمثيل التكاملي الآتي: , حيث دالة غير متناقصة ضمن المجال وتحقق الشرط . و قد تم ، في هذا الفضاء، البرهان على أن مجموعة قيم الدالي: عندما تكون كثيرة حدود في القرص ، هي قرص مغلق تم تحديد مركزه ونصف قطره . وقد تم أيضاً تحديد مستقرات بعض الداليات الأخرى في هذا الفضاء. This paper presents a certain method to determine the range of variability of some functionals defined in Generalized Caratheodory Class ( i.e the class of analytic functions in the unit disk of the form: , where is a nondecreasing function on the interval such that ). It has been proved that the range of variability of functional where is a polynomial in , is the closed disc with and precisely determined . Also the range of variability of some other functionals determined.Downloads
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