Sharp inequalities for the psi function and harmonic numbers

In this paper, two sharp inequalities for bounding the psi function $\psi$ and the harmonic numbers $H_n$ are established respectively, some results in [I. Muqattash and M. Yahdi, \textit{Infinite family of approximations of the Digamma function}, Math. Comput. Modelling \textbf{43} (2006), 1329\nobreakdash--1336.] are improved, and some remarks are given.