Article(electronic)#1December 13, 2021
Positivity of sums and integrals for n-convex functions via the Fink identity and new Green functions
In: Studia Universitatis Babeş-Bolyai. Mathematica, Volume 66, Issue 4, p. 613-627
ISSN: 2065-961X
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.