کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4619568 1339440 2010 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The Hermite–Hadamard inequality in Beckenbach's setting
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
The Hermite–Hadamard inequality in Beckenbach's setting
چکیده انگلیسی

The classical Hermite–Hadamard inequality gives a lower and an upper estimations for the integral average of convex functions defined on compact intervals, involving the midpoint and the endpoints of the domain. The aim of the present paper is to extend this inequality and to give analogous results when the convexity notion is induced by Beckenbach families. The key tool of the investigations is based on some general support theorems that are obtained via the pure geometric properties of Beckenbach families and can be considered as generalizations of classical support and chord properties of ordinary convex functions. The Markov–Krein-type representation of Beckenbach families is also investigated.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 364, Issue 2, 15 April 2010, Pages 366-383