On almost primes in Piatetski-Shapiro sequences

The author proves that for $0.9985<\gamma <1$, there exist infinitely many primes $p$ such that $[p^{1\mathrm{/}\gamma }]$ has at most 5 prime factors counted with multiplicity. This gives an improvement upon the previous results of Banks-Guo-Shparlinski and Xue-Li-Zhang.