14 research outputs found
On Kedlaya type inequalities for weighted means
In 2016 we proved that for every symmetric, repetition invariant and Jensen
concave mean the Kedlaya-type inequality holds for an
arbitrary ( stands for the arithmetic mean). We are going
to prove the weighted counterpart of this inequality. More precisely, if
is a vector with corresponding (non-normalized) weights
and denotes the weighted mean then, under
analogous conditions on , the inequality holds for every and such that the sequence
is decreasing.Comment: J. Inequal. Appl. (2018
Some New Refined General Boas-Type Inequalities
We state and prove a new refined Boas-type inequality in a setting
with a topological space and general σ-finite and finite Borel measures. As a
consequence of the result obtained, we derive a new class of Hardy- and Pólya-Knopp-type inequalities related to balls in ℝn and prove that constant factors
involved in their right-hand sides are the best possible