Uniqueness of Entire Functions that Share an Entire Function of Smaller Order with One of Their Linear Differential Polynomials

Xiao-Min Li; Hong-Xun Yi

doi:10.5666/KMJ.2016.56.3.763

Articles

Kyungpook Mathematical Journal -0001; 56(3): 763-776

Published online November 30, -0001

Uniqueness of Entire Functions that Share an Entire Function of Smaller Order with One of Their Linear Differential Polynomials

Xiao-Min Li¹, Hong-Xun Yi²

Department of Mathematics, Ocean University Of China, Qingdao, Shandong 266100, P. R. China¹Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China²

Received: December 29, 2011; Accepted: March 21, 2014

Abstract

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Abstract

We prove a uniqueness theorem of entire functions sharing an entire function of smaller order with their linear differential polynomials. The results in this paper improve the corresponding results given by Gundersen-Yang[4], Chang-Zhu[3], and others. Some examples are provided to show that the results in this paper are best possible.

Keywords: Entire functions, Shared values, Order of growth, Differential polynomials, Uniqueness theorems.