On inequality for convex function
type: Item
instance of: scholarly article
zbMATH Open document ID: 1049.26506
author: D. Yu. Mitin
publication date: 2001-08-08T00:00:00Z
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26D07
zbMATH DE Number: 1631469
zbMATH Keywords: convex function
zbMATH Keywords: inequality
zbMATH Keywords: Jensen inequality
MaRDI profile type: Publication
title: On inequality for convex function
published in: U Sviti Matematyky
review text: The author considers function \( f:\mathbb R\to\mathbb R \) which is convex on \([ a;b ] \). He proves that for \( x_{i}\in [ a,b ] ,m_{i}\geq 0(i=1,\ldots ,n),\sum ^{n}_{i=1}m_{i}\neq 0: \) NEWLINE\[NEWLINEf\left( \frac{\sum ^{n}_{i=1}m_{i}x_{i}}{\sum ^{n}_{i=1}m_{i}}\right) \leq \frac{\sum ^{n}_{i=1}m_{i}f\left( x_{i}\right) }{\sum ^{n}_{i=1}m_{i}}\leq \frac{f(a)-f(b)}{a-b}\cdot \frac{\sum ^{n}_{i=1}m_{i}x_{i}}{\sum ^{n}_{i=1}m_{i}}+\frac{af(b)-bf(a)}{a-b}NEWLINE\]NEWLINE It is shown that there exists a function such that these inequalities became identities.
description: scientific article; zbMATH DE number 1631469