Naslov
Positivity of sums and integrals for n-convex functions via the Fink identity

Autori
Khan, Asif R. ; Pečarić, Josip ; Praljak, Marjan ; Varošanec, Sanja

Izvornik
Turkish Journal of Mathematics (1300-0098) 43 (2019), 2; 579-594

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
n-convex function ; Fink identity ; Green function ; Čebyšev functional

Sažetak
We consider the positivity of the sum $\sum_{; ; ; ; i=1}; ; ; ; ^n p_iF(x_i)$ where F is a convex function of higher order as well as analogous results involving the integral $\int_a^bp(x)F(g(x))dx$. 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA