Naslov
Exponentially convex functions generated by Wulbert's inequality and Stolarsky-type means

Autori
Pečarić, Josip ; Perić, Ivan ; Roqia, G.

Izvornik
Mathematical and computer modelling (0895-7177) 55 (2012), 7/8; 1849-1857

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
3-Convex function; $log$-convex function; exponential convexity

Sažetak
Let $-\infty <a<b<\infty $. If $f$ is concave on $[a, b]$ and $\psi ^{; ; \prime }; ; $ is convex on the interval of integration, then D.E.Wulbert proved that \begin{; ; equation*}; ; \frac{; ; 1}; ; {; ; \delta _{; ; +}; ; -\delta _{; ; -}; ; }; ; \int\limits_{; ; \delta _{; ; -}; ; }; ; ^{; ; \delta _{; ; +}; ; }; ; {; ; % \psi ({; ; u)}; ; du}; ; \geq \frac{; ; 1}; ; {; ; b-a}; ; \int\limits_{; ; a}; ; ^{; ; b}; ; {; ; \psi (f(x))dx}; ; , \end{; ; equation*}; ; % where $\delta _{; ; -}; ; =\bar{; ; f}; ; -\sqrt{; ; 3}; ; \left(\|f\|_{; ; 2}; ; ^{; ; 2}; ; -\left(\bar{; ; f}; ; \right)^{; ; 2}; ; \right)^{; ; 1/2}; ; $, $\delta _{; ; +}; ; =\bar{; ; f}; ; +\sqrt{; ; 3}; ; \left(\|f\|_{; ; 2}; ; ^{; ; 2}; ; -\left(\bar{; ; f}; ; \right)^{; ; 2}; ; \right)^{; ; 1/2}; ; $, $\bar{; ; f}; ; =\frac{; ; 1}; ; {; ; b-a}; ; \int\limits_{; ; a}; ; ^{; ; b}; ; f(x)dx$ and $\|f\|_p=\left(\frac{; ; 1}; ; {; ; b-a}; ; \int_{; ; a}; ; ^{; ; b}; ; \left|f(x)\right|^pdx\right)^{; ; 1/p}; ; $. We define new Cauchy type means using a functional defined via above inequality and give some related results as applications.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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