Abstract
In this paper, we prove the following result: Let f be a nonconstant meromorphic function of finite order, p be a nonconstant polynomial, andc be a nonzero constant. If f, Delta _{c}f, and Delta_{c}^{n}f (nge 2) share ∞ and p CM, then fequiv Delta_{c}f. Our result provides a difference analogue of the result of Chang and Fang in 2004 (Complex Var. Theory Appl. 49(12):871–895, 2004).
Highlights
Introduction and main resultsIn this paper, we use the base notations of the Nevanlinna theory of meromorphic functions which are defined as follows [9, 18, 19].Let f be a meromorphic function
Throughout this paper, a meromorphic function always means meromorphic in the whole complex plane
Dt + n(0, f ) log r, t where n(t, f ) (n(t, f )) denotes the number of poles of f in the disc |z| ≤ t, multiples poles are counted according to their multiplicities. n(0, f ) (n(0, f )) denotes the multiplicity of poles of f at the origin
Summary
Introduction and main resultsIn this paper, we use the base notations of the Nevanlinna theory of meromorphic functions which are defined as follows [9, 18, 19].Let f be a meromorphic function. Definition 6 Let f and g be two meromorphic functions, and p be a polynomial. Theorem 1 Let f be a nonconstant meromorphic function, and a be a nonzero finite complex number.
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