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Uniform treatment of Jensen's type and converse Jensen's type inequalities for signed measures (CROSBI ID 544983)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Pečarić, Josip ; Perić, Ivan ; Rodić Lipanović, Mirna Uniform treatment of Jensen's type and converse Jensen's type inequalities for signed measures // Mathematical Inequalities and Applications 2008. Element, 2008. str. 117-117

Podaci o odgovornosti

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

engleski

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

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.

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

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Podaci o prilogu

117-117.

2008.

objavljeno

Podaci o matičnoj publikaciji

Mathematical Inequalities and Applications 2008

Element

Podaci o skupu

Mathematical Inequalities and Applications ; 2008

predavanje

08.06.2008-14.06.2008

Trogir, Hrvatska

Povezanost rada

Matematika