Additive and multiplicative structure of c${}^{\star }$-sets

It is known that for an IP${}^{\star }$ set $A$ in $\mathbb{N}$ and a sequence $<x_n{>}_{n=1}^{\mathrm{\infty }}$ there exists a sum subsystem $< y_{n}>{n=1}^{\infty}$of$< x{n}>{n=1}^{\infty}$suchthat$FS(< y_n>{n=1}^\infty)\cup FP(< y_n>_{n=1}^\infty)\subseteq A$. Similar types of results also have been proved for central* sets where the sequences have been taken from the class of minimal sequences. In this present work we will prove some analogues results for C${}^{\star }$-sets for a more general class of sequences.