Naslov
Recent research on Levinson’s inequality

Autori
Mićić, Jadranka ; Praljak, Marjan

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, pregledni

Knjiga
Frontiers in Functional Equations and Analytic Inequalities

Urednik/ci
Anastassiou, George ; Rassias, John Michael

Izdavač
Springer

Grad
Cham

Godina
2019

Raspon stranica
653-679

ISBN
978-3-030-28949-2

Ključne riječi
Levison's inequality ; converses of Levison's inequality ; Levison's operator inequality ; converses of Levison's operator inequality ; 3-convex functions at a point

Sažetak
In this paper we review the results on Levinson’s inequality and present some of its generalizations using several new approaches. We provide a probabilistic version for the family of 3-convex functions at a point. We also show that this is the largest family of continuous functions for which the inequality holds. From the obtained inequality, we derive new families of exponentially convex functions and related results. We also give a monotonic refinement of the probabilistic version of Levinson’s inequality. Levinson’s type inequality of Hilbert space operators is discussed as well for unital fields of positive linear mappings and a large class of functions. Order among quasi- arithmetic means is considered under similar conditions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA