an: Zbl 1195.26039
au: Cizmesija, A.; Krulic, K.; Pecaric, J.E.
ti: On a new class of refined discrete Hardy-type inequalities.
la: EN
so: Banach J. Math. Anal. 4, No. 1, 122-145, electronic only (2010).
py: 2010
dt: J
cc: *26D15 26B25
ut: carleman's inequality; inequality; discrete Hardy-type inequalities; refined
    inequality; convex function; exponential convexity
ab: Authors' abstract: 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.