Inequalities related to the Jensen inequality for strongly convex functions (CROSBI ID 664189)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Klaričić Bakula, Milica ; Nikodem, Kazimierz
engleski
Inequalities related to the Jensen inequality for strongly convex functions
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.
Strongly convex functions, Jensen inequality, Jensen-Steffensen inequality
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Podaci o prilogu
43-43.
2018.
objavljeno
Podaci o matičnoj publikaciji
Mathematical Inequalities and Applications 2018
Aglić Aljinović, Andrea ; Elezović, Neven ; Rodić, Mirna
Zagreb: Element
Podaci o skupu
Mathematical Inequalities and Applications, 2018.
predavanje
04.07.2018-08.07.2018
Zagreb, Hrvatska