Naslov
Inequalities related to the Jensen inequality for strongly convex functions

Autori
Klaričić Bakula, Milica ; Nikodem, Kazimierz

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

Izvornik
Mathematical Inequalities and Applications 2018 / Aglić Aljinović, Andrea ; Elezović, Neven ; Rodić, Mirna - Zagreb : Element, 2018, 43-43

Skup
Mathematical Inequalities and applications 2018

Mjesto i datum
Zagreb, Hrvatska, 04.07.2018. - 08.07.2018

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Strongly convex functions, Jensen inequality, Jensen-Steffensen inequality

Sažetak
A function f:I→R is called strongly convex with modulus c>0 if f(tx+(1-t)y)≤tf(x)+(1-t)f(y)-ct(1-t)(x-y)², for all x, y∈I and t∈[0, 1] (B. T. Polyak, 1966). Strongly convex functions are largely investigated in the literature since they are very useful in optimization theory, mathematical economics and approximation theory. Here we present several inequalities for strongly convex functions closely related to the Jensen inequality, such as the converse Jensen inequality and the Jensen-Steffensen inequality. We also consider those inequalities for set-valued strongly convex functions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA