A note on partial sharing of values of meromorphic functions with their shifts

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Charak, K. S.¹  Korhonen, R. J.²  Kumar, Gaurav¹ 

[1] Univ Jammu, Dept Math, Jammu 180006, India

[2] Univ Eastern Finland, Dept Phys & Math, FI-80101 Joensuu, Finland

关键词: Meromorphic functions;    Partial sharing of values;    Shift;    Difference operators;    Nevanlinna theory;   

DOI  :  10.1016/j.jmaa.2015.10.069

来源: Elsevier

【 摘 要 】

We introduce the notion of partial value sharing as follows. Let (E) over bar (a, f) be the set of zeros of f (z) - a(z), where each zero is counted only once and a is a meromorphic function, small with respect to f. A meromorphic function f is said to share a partially with a meromorphic function g if (E) over bar (a, f) subset of (E) over bar (a, g). We show that partial value sharing of f(z) and f(z + c) involving 3 or 4 values combined with an appropriate deficiency assumption is enough to guarantee that f(z) equivalent to f (z + c), provided that f(z) is a meromorphic function of hyper-order strictly less than one and c is an element of C. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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