Two mappings in connection to Hadamard's inequalities
type: Item
instance of: scholarly article
title: Two mappings in connection to Hadamard's inequalities
zbMATH Open document ID: 0758.26014
DOI: 10.1016/0022-247X(92)90233-4
author: Silvestru Sever Dragomir
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-01-16T00:00:00Z
review text: The author studies certain convex mappings which are connected to a given convex function \(f:[a,b]\to\mathbb{R}\). For example, let \[ H(t)={1\over b- a}\int^ b_ af(tx+(1-t)(a+b)/2)dx. \] Then \(H\) is convex on \([0,1]\); \(\inf H(t)=H(0)\), \(\sup H(t)=H(1)\) and \(H\) increases monotonically on \([0,1]\). This contains a refinement of the Jensen-Hadamard inequality \(H(0)\leq H(1)\leq(f(a)+f(b))/2\).
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 91568
zbMATH Keywords: convex functions
zbMATH Keywords: integral inequalities
zbMATH Keywords: Jensen-Hadamard inequality
reviewed by: József Sándor
MaRDI profile type: Publication
cites work: Q3488350
cites work: Hermite and convexity
cites work: Some integral inequalities
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description: scientific article; zbMATH DE number 91568