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Positivity of sums and integrals for n-convex functions via the Fink identity.
- Source :
-
Turkish Journal of Mathematics . 2019, Vol. 43 Issue 2, p579-594. 16p. - Publication Year :
- 2019
-
Abstract
- We consider the positivity of the sum Σi=1n ρiF(ξi), where F is a convex function of higher order, as well as analogous results involving the integral ∫aobo ρ(ξ)F(g(ξ))dξ . We use a representation of the function F via the Fink identity and the Green function that leads us to identities from which we obtain conditions for positivity of the above-mentioned sum and integral. We also obtain bounds for the integral remainders which occur in these identities, as well as corresponding mean value results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *INTEGRAL functions
*GREEN'S functions
*MEAN value theorems
*CONVEX functions
Subjects
Details
- Language :
- English
- ISSN :
- 13000098
- Volume :
- 43
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Turkish Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 136120399
- Full Text :
- https://doi.org/10.3906/mat-1810-129