Naslov
Jensen-type inequalities, Montgomery identity and higher order convexity

Autori
Bošnjak, Marija ; Krnić, Mario ; Pečarić, Josip

Izvornik
Mediterranean journal of mathematics (1660-5446) 19 (2022), 5; 230, 22

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Jensen inequality, Montgomery identity, Lah-Ribari\v c inequality, superadditivity, power mean

Sažetak
Motivated by some recent results known from the literature, in this paper we establish a class of Jensen-type inequalities referring to functions of an even degree of convexity. The main idea of proving our results is a transformation of the classical Jensen functional via the Montgomery identity which is suitable to study in companion with the higher order convexity. In such a way, we obtain superadditivity and monotonicity relations that correspond to the Jensen functional equipped with a function of an even degree of convexity. As an application, we obtain some new bounds for the differences of power means. Furthermore, we also establish some new H\"{;o};lder-type inequalities. Finally, we study the Lah-Ribari\v c inequality in the above described setting.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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