Classes of numerical sequences. (Q2770411)

The author generalizes some known classes of sequences. His main result is the following result: Assume that \(p\geq 1\) and a given positive sequence \(\rho:\{\rho_n\}\), for a certain positive \(\beta\), is quasi \(\beta\)-power monotone decreasing and simultaneously quasi \((1-\beta)\)-power monotone increasing. Then the following embedding relations hold: NEWLINE\[NEWLINEF_p(\rho) \subseteq F^*_p(\rho)\subseteq S_p(\rho)\subseteq S_p(A,\rho) \subseteq S_p(\delta,\rho)\subseteq F_p(\rho),NEWLINE\]NEWLINE (for various definitions reference may be made to the author's paper).