Naslov
Superadditivity of some Jensen-type functionals

Autori
Krnić, Mario ; Lovričević, Neda ; Pečarić, Josip

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

Izvornik
Book of abstracts - 5th Croatian Mathematical Congress, 18-21 June, 2012, Rijeka, Croatia / Crnković, Dean ; Mikulić Crnković, Vedrana ; Rukavina, Sanja (ur.). Rijeka: Department of Mathematics, University of Rijeka, 2012. / - , 2012, 62-62

Skup
5th Croatian Mathematical Congress

Mjesto i datum
Rijeka, Hrvatska, 18.06.2012. - 21.06.2012

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
superadditivity; Jensen inequality; functional; monotonicity; bounds

Sažetak
In 1996. S. S. Dragomir, J. Pečarić and L. E. Persson investigated discrete Jensen’s functional. They proved that, under the assumption of convexity of the involved function, this functional is superadditive and increasing on the set of all nonnegative weighted n-tuples. Motivated by their results, we prove the analogues ones for Jessen’s functional, as well as for McShane’s functional, which is a multidimensional generalization of Jessen’s functional. Consequently, we establish their lower and upper bounds expressed by the non weighted functionals of the same type. Such bounds enable us to obtain converses and refinements of the series of the classical inequalities, such are arithmetic-geometric inequality, Young’s and H¨older’s inequality in the difference and quotient form, as well as some other related inequalities.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA