Naslov
On a new class of refined discrete Hardy-type inequalities

Autori
Čižmešija, Aleksandra ; Krulić, Kristina ; Pečarić, Josip

Izvornik
Banach Journal of Mathematical Analysis (1735-8787) 4 (2010), 1; 122-145

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

Ključne riječi
inequalities; discrete Hardy-type inequalities; Carleman's inequality; refined inequalities; convex functions; exponential convexity

Sažetak
In this paper, we state, prove and discuss a new refined general weighted discrete Hardy-type inequality with a non-negative kernel, related to an arbitrary non-negative convex (or positive concave) function on a real interval and to a positive real parameter. As its consequences, obtained by rewriting it for various suitably chosen parameters, kernels, weights, and convex (or concave) functions, we derive new weighted and unweighted generalizations and refinements of some well-known inequalities, such as Carleman's inequality and the so-called Godunova's inequality. Finally, by employing exponential and logarithmic convexity, as special cases of the usual convexity, we obtain some further refinements of the inequalities mentioned above.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
Proceedings of the Conference Analysis, Inequalities and Homogenization Theory : in honor of Professor Lars-Erik Persson ; Luleå, 2009, Švedska ; Dag Lukkassen ; Lech Maligranda ; Annette Meidell ; Peter Wall (ur.)

POVEZANOST RADA