eigenvector problem encountered in markov chain / random walk with drift

Question

Is there a function $f: \mathbb{Z} \to \mathbb{R}^+$ where $$ pf_{1-n} + (1-p)f_{n-1} = f_{n} $$ for all $n \in \mathbb{Z}$? $p$ is some real number $0 < p < 1$.