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math.CA2013★ 2 cited
On negative results concerning Hardy means
Paweł Pasteczka
In the present paper we are going to prove some necessary condition for a mean to be Hardy. This condition is then applied to completely characterize the Hardy property among the G…
math.CA2013★ 3 cited
A new estimate of the difference among quasi-arithmetic means
Paweł Pasteczka
In the 1960s Cargo and Shisha proved some majorizations for the distance among quasi-arithmetic means (defined as f^{-1}(\sum_{i=1}^{n} w_i f(a_i) for any continuous, strictly mono…
math.CA2013★ 3 cited
On some type of Hardy's inequality involving generalized power means
Paweł Pasteczka
We discuss properties of certain generalization of Power Means proposed in 1971 by Carlson, Meany and Nelson. For any fixed parameter (k,s,q) and vector (v_1,...,v_n) they take the…