Weighted majorization inequalities for n-convex functions via extension of Montgomery identity using Green function

New identities and inequalities are given for weighted majorization theorem for n -convex functions by using extension of the Montgomery identity and Green function. Various bounds for the reminders in new generalizations of weighted majorization formulae are provided using Čebyšev type inequalities...

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Bibliographic Details
Published inArabian Journal of Mathematics Vol. 7; no. 2; pp. 77 - 90
Main Authors Aglić Aljinović, Andrea, Khan, Asif R., Pečarić, Josip E.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018
Springer
Springer Nature B.V
Subjects
Convex analysis
Convex functions
Green's functions
Inequalities
Inequalities (Mathematics)
Mathematical research
Mathematicians
Mathematics
Mathematics and Statistics
Theorems
26D20
26D15
26A51
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Summary:New identities and inequalities are given for weighted majorization theorem for n -convex functions by using extension of the Montgomery identity and Green function. Various bounds for the reminders in new generalizations of weighted majorization formulae are provided using Čebyšev type inequalities. Mean value theorems are also discussed for functional related to new results.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-017-0188-y