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## Bounds for the normalized Jensen-Mercer functional

Barić, Josipa; Matković, Anita
Bounds for the normalized Jensen-Mercer functional // Journal of Mathematical Inequalities, 3 (2009), 4; 529-541 doi:10.7153/jmi-03-52 (međunarodna recenzija, članak, znanstveni)

Naslov
Bounds for the normalized Jensen-Mercer functional

Autori
Barić, Josipa ; Matković, Anita

Izvornik
Journal of Mathematical Inequalities (1846-579X) 3 (2009), 4; 529-541

Ključne riječi
Jensen-Mercer functional; Jensen-Mercer inequality; convex functions; bounds

Sažetak
We introduce the normalized Jensen-Mercer functional M_{; ; ; ; ; ; n}; ; ; ; ; ; (f, x, p)=f(a)+f(b)-∑_{; ; ; ; ; ; i=1}; ; ; ; ; ; ⁿp_{; ; ; ; ; ; i}; ; ; ; ; ; f(x_{; ; ; ; ; ; i}; ; ; ; ; ; )-f(a+b-∑_{; ; ; ; ; ; i=1}; ; ; ; ; ; ⁿp_{; ; ; ; ; ; i}; ; ; ; ; ; x_{; ; ; ; ; ; i}; ; ; ; ; ; ) and establish the inequalities of type MM_{; ; ; ; ; ; n}; ; ; ; ; ; (f, x, q)≥M_{; ; ; ; ; ; n}; ; ; ; ; ; (f, x, p)≥mM_{; ; ; ; ; ; n}; ; ; ; ; ; (f, x, q), where f is a convex function, x=(x₁, …, x_{; ; ; ; ; ; n}; ; ; ; ; ; ) and m and M are real numbers satisfying certain conditions. We prove them for the case when p and q are nonnegative n-tuples and when p and q satisfy the conditions for the Jensen-Steffensen inequality. We also give their integral versions in both cases.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
177-1170889-1287 - Konveksne funkcije i primjene (Marko Matić, )

Ustanove
Fakultet elektrotehnike, strojarstva i brodogradnje, Split,
Prirodoslovno-matematički fakultet, Split

#### Časopis indeksira:

• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI

#### Uključenost u ostale bibliografske baze podataka:

• MathSciNet
• Zentrallblatt für Mathematik/Mathematical Abstracts