\(P\)-functions, quasi-convex functions, and Hadamard-type inequalities
type: Item
instance of: scholarly article
title: \(P\)-functions, quasi-convex functions, and Hadamard-type inequalities
zbMATH Open document ID: 0939.26009
author: Charles E. M. Pearce
author: A. M. Rubinov
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-03-19T00:00:00Z
review text: A nonnegative function \(f\) defined on \([a,b]\) is said to be a \(P\)-function if \[ f(tx+ (1- t)y)\leq f(x)+ f(y),\quad x,y\in [a,b],\quad t\in [0,1]. \] The authors show that the set of all \(P\)-functions on \([a,b]\) is the least set closed under pointwise sum, supremum, and convergence and containing the class of all nonnegative quasi-convex functions. Hadamard type inequalities for \(P\)-functions are also presented.
reviewed by: Ioan Raşa
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 1398598
zbMATH Keywords: \(P\)-functions
zbMATH Keywords: quasi-convex functions
zbMATH Keywords: Hadamard type inequalities
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6593
OpenAlex ID: W1968476607
cites work: Q4858718
cites work: Quasi-convex functions and Hadamard's inequality
cites work: Q3126366
cites work: Seven Kinds of Convexity
cites work: Q4336961
cites work: Q4339231
DOI: 10.1006/JMAA.1999.6593
description: scientific article; zbMATH DE number 1398598