Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure (CROSBI ID 235213)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Mikić, Rozarija ; Pečarić, Josip ; Rodić, Mirna
engleski
Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure
We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi’s inequality. The obtained results are then applied for establishing new mean-value theorems. The results from this paper represent a generalization of several recent results.
Jensen’s inequality ; converse Jensen’s inequality ; Hermite-Hadamard’s inequality ; Giaccardi’s inequality ; Levinson’s inequality ; Green function ; mean-value theorems
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Podaci o izdanju
(1)
2017.
4-1-4-
objavljeno
1029-242X
10.1186/s13660-016-1274-y