Naslov
Generalization of Levinson's inequality

Autori
Baloch, Imran Abbas ; Pečarić, Josip ; Praljak, Marjan

Izvornik
Journal of Mathematical Inequalities (1846-579X) 9 (2015), 2; 571-586

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

Ključne riječi
Levinson’s inequality; 3-convex functions; divided differences

Sažetak
Mercer gave a generalization of Levinson’s inequality that replaces the assumption of symmetry of the two sequences with a weaker assumptions of equality of variances. Witkowski further loosened this assumption and extended the result to the class of 3-convex functions. We generalize these results to a newly defined, larger class of functions. We also prove the converse in case the function is continuous. In particular, we show that if Levinson’s inequality holds under Mercer’s assumptions, then the function is 3-convex.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA