Turkish Journal of Mathematics
DOI
10.3906/mat-1810-129
Abstract
We consider the positivity of the sum $\sum_{i=1}^n\rho_i\digamma(\xi_i)$, where $\digamma$ is a convex function of higher order, as well as analogous results involving the integral $\int_{a_0}^{b_0}\rho(\xi)\digamma(g(\xi))d\xi$. We use a representation of the function $\digamma$ 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.
Keywords
$n$-convex functions, Fink identity, Green function, \v{C}eby\v{s}ev functional
First Page
579
Last Page
594
Recommended Citation
KHAN, ASIF R.; PECARIC, JOSIP; PRALJAK, MARJAN; and VAROSANEC, SANJA
(2019)
"Positivity of sums and integrals for $n$-convex functions via the Fink identity,"
Turkish Journal of Mathematics: Vol. 43:
No.
2, Article 2.
https://doi.org/10.3906/mat-1810-129
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss2/2
