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
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