Naslov
Weighted Popoviciu type inequalities via generalized Montgomery identities

Autori
Butt, Saad Ihsan ; Pečarić, Josip

Izvornik
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti (1845-4100) 19 (2015); 69-89

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

Ključne riječi
convex function; divided difference; generalized Montgomery identity; Čebyšev functional; Gruss inequality; Ostrowski inequality; exponential convexity

Sažetak
We obtained useful identities via generalized Montgomery identities by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate bounds for terms related to the generalization of the Popoviciu inequality using inequalities for the Čebyšev functional. Some results related to the Gruss and Ostrowski type inequalities are constructed. Furthermore, we also construct new families of exponentially convex functions and Cauchy type means by looking at linear functionals associated with the obtained inequalities.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA