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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2018, Issue 4(37), Pages 98–102
(Mi pfmt611)
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This article is cited in 1 scientific paper (total in 1 paper)
MATHEMATICS
$\mathfrak{K}_{\varphi}\mathfrak{K}_{\psi}$-convex functions and generalizations of classical inequalities
V. I. Murashkaa, S. M. Gorskyb, Ya. I. Sandryhailac a F. Scorina Gomel State University
b Saint Petersburg Academic University of the Russian Academy of Sciences, St. Petersburg
c Belarussian State University
Abstract:
A function $f$ is called $\mathfrak{MN}$-convex, if for any $x$ and $y$ from the domain of $f$ inequality $f(\mathfrak{M}(x,y))\leqslant\mathfrak{N}(f(x),f(y))$ holds, where $\mathfrak{M}$ and $\mathfrak{N}$ are means. In this paper geometric interpretation of $\mathfrak{MN}$-convexity of a function is obtained, where $\mathfrak{M}$ and $\mathfrak{N}$ are Kolmogorov's means. For such functions analogies of rearrangement, Popovicu's, Chebyshev's sum and Hermite–Hadamar's inequalities are obtained.
Keywords:
convex function, $\mathfrak{MN}$-convex function, rearrangement inequality, Popovicu's inequality, Chebyshev's sum inequality, Jensen's inequality, Hermite–Hadamar's inequality.
Received: 31.07.2018
Citation:
V. I. Murashka, S. M. Gorsky, Ya. I. Sandryhaila, “$\mathfrak{K}_{\varphi}\mathfrak{K}_{\psi}$-convex functions and generalizations of classical inequalities”, PFMT, 2018, no. 4(37), 98–102
Linking options:
https://www.mathnet.ru/eng/pfmt611 https://www.mathnet.ru/eng/pfmt/y2018/i4/p98
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Abstract page: | 220 | Full-text PDF : | 141 | References: | 17 |
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