Abstract
Let f and g be two nonconstant meromorphic functions. Shared value problems related to f and g are investigated in this paper. We give sufficient conditions in terms of weighted value sharing which imply that f is a linear transformation or inversion transformation of g. We also investigate the uniqueness problem of meromorphic functions with their difference operators and derivatives sharing some values.
Highlights
1 Introduction and main results Throughout this paper, a meromorphic function is assumed to be meromorphic in the whole complex plane
The basic notations and results of Nevanlinna value distribution theory of meromorphic function are assumed to be known to the reader; see, e.g., [10, 21]
N(k+1(r, f the counting function of a points of f with multiplicity k, where each a point is counted according to its multiplicity
Summary
We say that f and g share the value a IM (ignoring multiplicities), if f and g have the same a point. If f and g have the same a point with the same multiplicities, we say f , g share the value a CM (counting multiplicities). Let k be a positive integer, we denote by. K, where each a point is counted according to its multiplicity
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