On Some Intermediate Mean Values

On Some Intermediate Mean Values

We give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class of mean values where are continuously differentiable convex functions satisfying the relation ,  . Then we asked for a characterization of such that the inequalities or hold for e...

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Main Author: Slavko Simic
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2013/283127
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spelling doaj-71d681af1db141959587ed83873173c72020-11-24T22:45:48ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/283127283127On Some Intermediate Mean ValuesSlavko Simic0Mathematical Institute SANU, Kneza Mihaila 36, 11000 Belgrade, SerbiaWe give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class of mean values where are continuously differentiable convex functions satisfying the relation ,  . Then we asked for a characterization of such that the inequalities or hold for each positive , where are the harmonic, arithmetic, logarithmic, and identric means, respectively. For a subclass of with , this problem is thoroughly solved.http://dx.doi.org/10.1155/2013/283127
collection DOAJ
language English
format Article
sources DOAJ
author Slavko Simic
spellingShingle Slavko Simic
On Some Intermediate Mean Values
International Journal of Mathematics and Mathematical Sciences
author_facet Slavko Simic
author_sort Slavko Simic
title On Some Intermediate Mean Values
title_short On Some Intermediate Mean Values
title_full On Some Intermediate Mean Values
title_fullStr On Some Intermediate Mean Values
title_full_unstemmed On Some Intermediate Mean Values
title_sort on some intermediate mean values
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2013-01-01
description We give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class of mean values where are continuously differentiable convex functions satisfying the relation ,  . Then we asked for a characterization of such that the inequalities or hold for each positive , where are the harmonic, arithmetic, logarithmic, and identric means, respectively. For a subclass of with , this problem is thoroughly solved.
url http://dx.doi.org/10.1155/2013/283127
work_keys_str_mv AT slavkosimic onsomeintermediatemeanvalues
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