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Generalization of Jensen's inequality by Euler's identity and related results (CROSBI ID 206045)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Aras-Gazić, Gorana ; Pečarić, Josip ; Vukelić, Ana Generalization of Jensen's inequality by Euler's identity and related results // Advanced Studies in Contemporary Mathematics, 24 (2014), 2; 247-268

Podaci o odgovornosti

Aras-Gazić, Gorana ; Pečarić, Josip ; Vukelić, Ana

engleski

Generalization of Jensen's inequality by Euler's identity and related results

In this paper we consider $n$-convex functions. Using Euler's identity, the result concerning for Jensen's inequality and converses of Jensen's inequality for signed measure are presented. As a consequence, also the results concerning to the Hermite-Hadamard inequalities are presented. Using these inequalities, we produce new exponentially convex functions. Finally, we give several examples of the families of functions for which the obtained results can be applied.

Bernoulli polynomials ; Bernoulli numbers ; Euler identity ; Jensen inequality ; Hermite-Hadamard inequality ; $n$-convex function ; Cauchy type mean value theorems ; $n$-exponential convexity ; exponential convexity ; log-convexity ; means

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Podaci o izdanju

24 (2)

2014.

247-268

objavljeno

1229-3067

2508-7908

Povezanost rada

Matematika

Indeksiranost