Refinements of the majorization-type inequalities via green and fink identities and related results

In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type in...

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Bibliographic Details
Published inMathematica Slovaca Vol. 68; no. 4; pp. 773 - 788
Main Authors Khalid, Sadia, Pečarić, Josip, Vukelić, Ana
Format Journal Article
LanguageEnglish
Published Heidelberg De Gruyter 28.08.2018
Walter de Gruyter GmbH
Subjects
26D15
convex function
divided difference
exponential convexity
Fink’s identity
Functionals
Green’s function
Grüss-type inequality
Inequalities
Inequality
logarithmic convexity
majorization
Ostrowski-type inequality
Primary 26A51
Sherman’s inequality
Čebyšev functional
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Summary:In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0139-9918
1337-2211
DOI:10.1515/ms-2017-0144