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Superquadracity on the coordinates


Banić, Senka; Klaričić Bakula, Milica
Superquadracity on the coordinates // Mathematical Inequalities and Applications 2014. One Thousand Papers Conference, Book of Abstracts / Andrić, Maja ; Klaričić Bakula, Milica ; Varošanec, Sanja (ur.).
Zagreb: Element, 2014. str. 24-24 (predavanje, međunarodna recenzija, sažetak, znanstveni)


Naslov
Superquadracity on the coordinates

Autori
Banić, Senka ; Klaričić Bakula, Milica

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

Izvornik
Mathematical Inequalities and Applications 2014. One Thousand Papers Conference, Book of Abstracts / Andrić, Maja ; Klaričić Bakula, Milica ; Varošanec, Sanja - Zagreb : Element, 2014, 24-24

Skup
Mathematical Inequalities and Applications 2014. One Thousand Papers Conference

Mjesto i datum
Trogir, Hrvatska, 22-26.06.2014.

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Functions superquadratic on the coordinates; functions convex on the coordinates; Jensen's inequality; Slater's inequality
(Functions superquadratic on the coordinates; Functions convex on the coordinates; Jensen's inequality; Slater's inequality)

Sažetak
In 2004 Abramovich, Jameson and Sinnamon introduced a new interesting class of functions: the class of superquadratic functions. Three years later Abramovich, Banić and Matić generalized this concept for the functions in several variables. The class of superquadratic functions is strongly related to the class of convex functions: it can be proved that any nonnegative superquadratic function is convex. The refinements of many important inequalities for convex functions easily follow as special cases when considered superquadratic functions are nonnegative. Here we introduce the class of functions in two variables which are superquadratic on the coordinates. It can be proved that a function which is superquadratic on the coordinates is not necessarily superquadratic and vice versa. The important property of this class of functions is the fact that any nonnegative function superquadratic on the coordinates is also convex on the coordinates. This property enables us to give refinements of some of the previously established results for the functions which are convex on the coordinates. Particularly, we obtain versions of Jensen's and Slater's inequality for functions superquadratic on the coordinates which refine corresponding result obtained by Klaričić Bakula and Pečarić. As an application we use these results to derive several Hölder type inequalities with non conjugate exponents.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
5435

Ustanove
Fakultet građevinarstva, arhitekture i geodezije, Split,
Tekstilno-tehnološki fakultet, Zagreb,
Prirodoslovno-matematički fakultet, Split