Naslov
Uniform treatment of Jensen's type and converse Jensen's type inequalities for signed measures

Autori
Pečarić, Josip ; Perić, Ivan ; Rodić Lipanović, Mirna

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Mathematical Inequalities and Applications 2008 / - : Element, 2008, 117-117

Skup
Mathematical Inequalities and Applications 2008

Mjesto i datum
Trogir, Hrvatska, 08.06.2008. - 14.06.2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Jensen's inequality; Green function; Jensen-Steffensen's inequality; converses of Jensen's inequality; Hermite-Hadamard's inequality

Sažetak
The main purpose of this talk is to give the uniform treatment of Jensen's type inequalities. Using the Green function, we give some new conditions for Jensen's inequality to hold. Integral and discrete case are presented. In the discrete version we get the generalization of the results from [A. McD. Mercer: An "error term" for the Ky Fan inequality, J. Math. Anal. Appl. 220 (1998) 774-777.] and [A. McD. Mercer: Some new inequalities involving elementary mean values, J. Math. Anal. Appl. 229 (1999) 677-681.], and in integral version the results from [J. E. Pečarić, I. Perić and H. M. Srivastava: A family of the Cauchy type mean-value theorems, J. Math. Anal. Appl. 306 (2005) 730-739.]. Using the same method we also give adequate results for converses of the Jensen inequality. As a consequence, the results concerning the Hermite-Hadamard inequalities are also presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA