Naslov
Generalization of Jensen's and Jensen- Steffensen's inequalities and their converses by Hermite polynomials and majorization theorem

Autori
Aras-Gazić, Gorana ; Pečarić, Josip ; Vukelić, Ana

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

Izvornik
Book of Abstracts of the conference Mathematical Inequalities and Applications 2015 / Andrić, Maja ; Tipurić-Spužević, Sanja ; Varošanec, Sanja - Mostar : Faculty of Science and Education, University of Mostar, 2015, 21-21

Skup
Conference Mathematical Inequalities and Applications 2015

Mjesto i datum
Mostar, Bosna i Hercegovina, 11.11.2015. - 15.11.2015

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Majorization ; Green function ; Jensen inequality ; Jensen-Steffensen inequality ; n-convex function ; Hermite interpolating polynomial ; Cauchy type mean value theorems ; n-exponential convexity ; exponential convexity ; log-convexity ; means

Sažetak
In this paper, using majorization theorems, Hermite's interpolating polynomials and conditions on Green's function we obtain results concerning Jensen's and Jensen- Steffensen's inequalities and their converses in both the integral and the discrete case. We use these generalizations to construct a linear functional and we present mean value theorems and n-exponential convexity which leads to exponential convexity and then log-convexity for these functionals. We give some families of functions which enable us to construct a large families of functions that are exponentially convex and also give Stolarsky type means with their monotonicity.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA