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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 .

discrete dynamics in nature and society

Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-Shift

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