Schur-Convexity of Averages of Convex Functions

The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasiarithmetic mean is studied. Relation to some already published result...

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Published inJournal of inequalities and applications Vol. 2011; no. 1; p. 581918
Main Authors Culjak, Vera, Franjic, Iva, Roqia Ghulam, Pecaric, Josip
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.01.2011
BioMed Central Ltd
SpringerOpen
Subjects
Mathematical functions
Mathematics
Studies
Online AccessGet full text
ISSN1025-5834
1029-242X
1029-242X
DOI10.1186/1029-242X-2011-581918

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Summary:The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasiarithmetic mean is studied. Relation to some already published results is established, and some applications of the extended result are given. Furthermore, Schur-convexity of functions connected to the Hermite-Hadamard inequality is investigated. Finally, some results on convexity and Schur-convexity involving divided difference are considered.
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ISSN:1025-5834
1029-242X
1029-242X
DOI:10.1186/1029-242X-2011-581918