Positivity of sums and integrals for n-convex functions via the Fink identity and new Green functions
2021 ◽
Vol 66
(4)
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pp. 613-627
Keyword(s):
We consider positivity of sum $\sum_{i=1}^np_if(x_i)$ involving convex functions of higher order. Analogous for integral $\int_a^bp(x)f(g(x))dx$ is also given. Representation of a function $f$ via the Fink identity and the Green function leads us to identities for which we obtain conditions for positivity of the mentioned sum and integral. We obtain bounds for integral remainders which occur in those identities as well as corresponding mean value theorems.
1982 ◽
Vol 383
(1785)
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pp. 313-332
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Keyword(s):
2017 ◽
Vol 32
(14)
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pp. 1750074
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Keyword(s):
2016 ◽
Vol 472
(2191)
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pp. 20160255
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1993 ◽
Vol 50
(11)
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pp. 2491-2512
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2018 ◽
Vol 11
(04)
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pp. 1850060
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Keyword(s):
1968 ◽
Vol 49
(5)
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pp. 2002-2008
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Keyword(s):
1967 ◽
Vol 47
(8)
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pp. 2728-2735
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Keyword(s):