Abstract. It is proved that the class of quasi-monotonic sequences with the additional assumption $\Sigma c_n/n < \infty $ is not comparable to the class of $\delta $-quasi-monotonic sequences with the assumption $\Sigma n^\gamma\delta _n < \infty $, $\gamma >0$; furthermore none of them is comparable to the class of sequences of rest bounded variation.

AMS Subject Classification (1991): 26D15, 40-99, 42A20

Keyword(s): Inequalities, embedding relations, sums, \delta, -quasi monotone sequences, R^+_0 BV, -sequences, sine and cosine series

Received January 30, 2001. (Registered under 2862/2009.)