Email this article ON UNIQUENESS OF MEROMORPHIC FUNCTIONS PARTIALLY SHARING VALUES WITH THEIR SHIFTS
About this article
Received: 26/07/19 Revised: 18/08/20 Published: 19/08/20Authors
1. Nguyen Hai Nam
, National University of Civil Engineering2. Nguyen Minh Nguyet, National University of Civil Engineering
3. Nguyen Thi Ngoc, National University of Civil Engineering
4. Vu Thi Thuy, National University of Civil Engineering
Abstract
In 1926, R. Nevanlinna showed that two distinct nonconstant meromorphic functions and on the complex plane share five distinct values then on whole If a meromorpic function with hyper-order less than 1 and its shifts share four distinct values or share partially four small periodic functions in the complex plane, then whether or not. Our aim is to study uniqueness of such meromorphic functions. For our purpose, we use techniques in Nevanlinna theory by estimating the counting functions and use the property of defect relation of values on the complex plane. Let be four small periodic functions with period c in the complex plane for . Then we prove a result as folows: Assume that meromorphic function of hyper-order less than 1 with its shift share CM, shares partially IM and reduced defect of at is maximal. Then under an appropriate deficiency assumption, for all Our result is a continuation of previous works of the authors and provides an understanding of the meromorphic functions of hyper-order less than 1.
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