Geodesic
$\mathfrak{H}_p\mathfrak{H}_q$-convex functions and generalization of the H\"older, Minkowski, and Muirhead inequalities
Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 61-66.

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Let $\mathfrak{M}$, $\mathfrak{N}$ be any means. Let $\mathfrak{H}_p$ be a power mean with exponent $p$. A function $f$ is called $\mathfrak{MN}$-convex if for any $x$ and $y$ from the domain of $f$ the inequality$f(\mathfrak{M}(x,y))\leqslant\mathfrak{N}(f(x),f(y))$ holds. In this paper the method of constructing $\mathfrak{H}_p\mathfrak{H}_q$-convex functions is proposed. For such functions generalizations of Cauchy–Schwarz, Hölder, Minkowski, Mahler, and Muirhead inequalities are obtained.
Keywords: $\mathfrak{MN}$-convex function, Cauchy–Schwarz inequality, Hölder inequality, Minkowski inequality, Mahler inequality, Muirhead inequality, Hölder mean. 
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     author = {S. M. Gorsky and V. I. Murashka},
     title = {$\mathfrak{H}_p\mathfrak{H}_q$-convex functions and generalization of the {H\"older,} {Minkowski,} and {Muirhead} inequalities},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {61--66},
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     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2020_3_a9/}
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S. M. Gorsky; V. I. Murashka. $\mathfrak{H}_p\mathfrak{H}_q$-convex functions and generalization of the H\"older, Minkowski, and Muirhead inequalities. Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 61-66. http://geodesic.mathdoc.fr/item/PFMT_2020_3_a9/

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