Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Theirq-Shift

We investigate value distribution and uniqueness problems of meromorphic functions with their -shift. We obtain that if is a transcendental meromorphic (or entire) function of zero order, and is a polynomial, then has infinitely many zeros, where , is nonzero constant, and (or ). We also obtain that zero-order meromorphic function share is three distinct values IM with its -difference polynomial , and if , then .