Naslov
Some remarks on inequalities of L. Iliev

Autori
Pečarić, Josip ; Varošanec, Sanja

Izvornik
Mathematica balkanica (0205-3217) 6 (1992), 2; 183-186

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

Ključne riječi
convex sequence; the majorization theorem

Sažetak
The sequence (a_n) belongs to the class \alpha if for any polynomial b which has only real zeros, the polynomial b*a_n also has only real zeros. We proved that if (a_n) \in \alpha, x_i, y_i integers, p_i are real and x_1 \geq ...\geq x_n, y_1\geq ... \geq y_n, then inequality \prod_{;r=1};^n |a_{;x_r};|^{;p_r}; \geq \prod_{;r=1};^n |a_{;y_r};|^{;p_r}; holds if and only if \sum_{;r=1};^k p_r x_r \leq \sum_{;r=1};^k p_r y_r, for k=1, 2, ..., n-1 and \sum_{;r=1};^n p_r x_r = \sum_{;r=1};^n p_r y_r. This result is applied on some entire functions and we get some new inequalities for it.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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