Bounds for the Normalized Jensen-Mercer Functional (CROSBI ID 541248)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Barić, Josipa ; Matković, Anita
engleski
Bounds for the Normalized Jensen-Mercer Functional
We introduce the normalized Jensen-Mercer functional M_{; ; ; n}; ; ; (f, x, p)=f(a)+f(b)-∑ _{; ; ; i=1}; ; ; ⁿ p_{; ; ; i}; ; ; f(x_{; ; ; i}; ; ; )-f(a+b-∑ _{; ; ; i=1}; ; ; ⁿ p_{; ; ; 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 cases when p and q are nonnegative n-tuples and when p and q satisfy the conditions as for the Jensen-Steffensen inequality. We also give their integral versions in both cases.
Jensen-Mercer functional; Jensen-Mercer inequality; convex functions; bounds
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Podaci o prilogu
36-36.
2008.
objavljeno
Podaci o matičnoj publikaciji
Mathematical inequalities and applications 2008 : conference in honour of Professor Josip Pečarić on the occasion of his 60th birthday : book of abstracts
Čižmešija, Aleksandra ; Varošanec Sanja
Zagreb: Element
Podaci o skupu
Mathematical Inequalities and Applications ; 2008
predavanje
08.06.2008-14.06.2008
Trogir, Hrvatska