A note on power of meromorphic function and its shift operator of certain hyper-order sharing one small function and a value

In this article, we obtain two results on $n$ the power of a meromorphic function and its shift operator sharing small together with value which improve complement some earlier results. particular, more or less have improved extended Qi-Yang [Meromorphic functions that share values their shifts $n$-th order differences, Analysis Math., 46(4)2020, 843-865] by dispelling superfluous conclusions in them.