Naslov
On superquadratic functions

Autori
Banić, Senka ; Varošanec, Sanja

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Zbornik Četvrtog hrvatskog matematičkog kongresa / Scitovski, Rudolf - Osijek : Hrvatsko matematičko društvo, 2008, 16-17

Skup
Fourth Croatian Mathematical Congres

Mjesto i datum
Osijek, Hrvatska, 17.06.2008. - 20.06.2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
convex functions; Hermite-Hadamard's inequality; Jensen's inequality; superquadratic functions

Sažetak
Recently a new interesting class of functions strongly related to convex functions has been introduced. It is named superquadratic functions. We say that the function ϕ is superquadratic if for any x≥ 0 there exists C(x)∈ R such that ϕ (y)≥ ϕ (x)+C(x)(y-x)+ϕ (|y-x|), ∀ y≥ 0. It can be proved that a superquadratic function which is also nonnegative is convex. Using some established characterisations and properties of this new class of functions we obtain variants of several well known inequalities for superquadratic functions. In a special case when superquadratic function is nonnegative we get refinements of known results related to convex functions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA