the integral version of popoviciu's inequality on the real line

الصيغة التكاملية لمتباينة بوبوفيتشيو على خط الأعداد الحقيقية

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ID: 137112
2016
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Abstract
T. Popoviciu has proved in 1965 an interesting characterization of the convex functions of one real variable, relating the arithmetic mean of its values and the values taken at the barycenters of certain subfamilies of the given family of points. The aim of our paper is to prove an integral analogue in the framework of absolutely continuous probability measures on the real line.
أثبت ت. بوبوفيتشيو عام 1965 توصيفاً مثيراً للاهتمام للدوال المحدبة لمتغير حقيقي واحد، يربط بين الوسط الحسابي لقيمها والقيم المأخوذة عند مراكز الثقل لعائلات جزئية معينة من عائلة النقاط المعطاة. وتهدف ورقتنا البحثية إلى إثبات نظير تكاملي في إطار مقاييس الاحتمال المطلقة الاستمرار على المستقيم الحقيقي.
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niculescu2016mathematicsthe Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
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Journal mathematics and its applications: annals of the academy of romanian scientists
Year 2016
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