Meromorphic Function Sharing Sets with Its Difference Operator or Shifts

Let $f$ be a nonconstant meromorphic function, $c \in \Bbb{C}$, and let $a(z)(\not\equiv 0)\in S(f)$ be a meromorphic function. If $f (z)$ and $P(z, f(z))$ share the sets $\{a(z),-a(z)\}$, $\{0\}$ CM almost and share $\{\infty\}$ IM almost, where $P(z, f(z))$ is defined as (1.1), then $f(z)\equiv \pm P(z,f(z))$ or $f(z)P(z, f(z))\equiv \pm a^{2}(z)$. This extends the results due to Chen and Chen (2013), Liu (2009) and Yi (1987).