A characterization of convex \(_\phi \)-functions (Q2901942)
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scientific article; zbMATH DE number 6062439
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of convex \(_\phi \)-functions |
scientific article; zbMATH DE number 6062439 |
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31 July 2012
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inequalities
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modulars
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Musielak-Orlicz spaces
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convexity
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isotonicity
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projections
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antiprojections
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0.95588434
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0.94083416
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0.9304688
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A characterization of convex \(_\phi \)-functions (English)
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By improving results from [\textit{G. Isac} and \textit{G. Lewicki}, Acta Math. Hung. 83, No. 4, 293--301 (1999; Zbl 0938.46025)] and [\textit{B. Micherda}, Math. Inequal. Appl. 4, No. 4, 599--608 (2001; Zbl 1023.46027)], the author shows that, under some restrictive assumptions on the \(\varphi\)-function \(\Phi\), the Musielak-Orlicz modular function generated by \(\Phi\) satisfies the lower property of four elements [\textit{G. Isac}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 454, 365--379 (1995; Zbl 0848.46008)] as well as the upper property of four elements [\textit{G. Isac} and \textit{L.-E. Persson}, Math. Inequal. Appl. 1, No. 1, 85--97 (1998; Zbl 0904.46010)] if and only if the function \(\Phi\) is convex with respect to its second variable.
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