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Register a new userOn Markov and Bernstein inequalities in weighted for real polynomials
دراسة متراجحة ماركوف –بيرنشتين التّكاملية في الفضاء الموزّن لكثيرات الحدود الحقيقية
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Tishreen University ورقة بحثية
Publication date
2015
fields
Mathematics
and research's language is
العربية
Created by
Shamra Editor
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قمنا في هذا البحث بدراسة متراجحة ماركوف –بيرنشتين التّكاملية لكثيرات الحدود الجبرية من الدّرجة 2 على الأكثر مع دالة الوزن في الفضاء على ،ثمّ تمّتدراسة متراجحة ماركوف – بيرنشتين لكثيرات الحدود المثلثية ،و بعد ذلك توصلنا إلى متراجحة ماركوف –بيرنشتين لكثيرات الحدود الجبرية من الدّرجة مع دالة الوزن.
In this research , we studied Markov -Bernstein inequalities for polynomials of degree at most with weight function in space on ,then we studied Markov -Bernstein inequalities for trigonometric polynomials .After that, we obtained the Markov –Bernstein inequalities for algebraicpolynomials of degree with weight function .
Artificial intelligence review:
Research summary
في هذا البحث، قام الباحثون بدراسة متراجحات ماركوف – بيرنشتين التكاملية لكثيرات الحدود الجبرية من الدرجة 2m على الأكثر مع دالة الوزن (1 + x^2) في فضاء Lp على المجال [0, +∞[. كما تم دراسة متراجحات ماركوف – بيرنشتين لكثيرات الحدود المثلثية. ونتيجة لذلك، توصلوا إلى متراجحات ماركوف – بيرنشتين لكثيرات الحدود الجبرية من الدرجة m مع دالة الوزن (1 + x^2) على نفس المجال. تهدف هذه الدراسة إلى تقديم متراجحات تكاملية يمكن استخدامها في العديد من مسائل التحليل الرياضي، وخاصة في نظرية التقريب. تم استخدام طرق رياضية متنوعة لتحقيق النتائج المطلوبة، وتم تقديم تعريفات ومبرهنات تدعم النتائج المستخلصة.
Critical review
دراسة نقدية: على الرغم من أن البحث يقدم مساهمات قيمة في مجال التحليل الرياضي، إلا أنه يفتقر إلى تطبيقات عملية واضحة يمكن أن تساعد في فهم أهمية النتائج في سياقات حقيقية. كما أن الدراسة تركز بشكل كبير على الجانب النظري دون تقديم أمثلة تطبيقية توضح كيفية استخدام المتراجحات في مسائل حقيقية. بالإضافة إلى ذلك، كان من الممكن تحسين العرض من خلال تقديم رسوم بيانية أو جداول توضيحية لتسهيل فهم النتائج.
Questions related to the research
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ما هي الأهمية الرئيسية لهذا البحث؟
تكمن أهمية البحث في استخدام نتائجه في العديد من مسائل التحليل الرياضي، وخاصة في مسائل نظرية التقريب.
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ما هي الدوال التي تم دراستها في هذا البحث؟
تم دراسة كثيرات الحدود الجبرية والمثلثية مع دوال الوزن المختلفة.
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ما هي الفضاءات التي تم استخدام المتراجحات فيها؟
تم استخدام المتراجحات في فضاء Lp الموزّن.
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ما هي التوصيات التي قدمها الباحثون في نهاية الدراسة؟
أوصى الباحثون بإجراء دراسات إضافية على فضاءات موزّنة أخرى مثل فضاء أورليتش.
References used
GUVEN,A; ISRAFILOV,D-M . Multiplier theorems in weighted Smirnov spaces. J.Korean Math soc,45,No6,2008,pp.1535-1548
T.Kilgore,Interpolation properties of polynomials of degree at most 2 weighted by ,East J.Approx.7(2001),no.1,9-25
T.Kilgore,Markov and Bernstein inequalities in for some weighted algebraic and trigonometric polynomails ,Journal of Inequalities and Application .4(2005),413-421
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