Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(4): 1213-1235

Printed July 31, 2016

https://doi.org/10.4134/BKMS.b150609

Copyright © The Korean Mathematical Society.

Meromorphic functions sharing four values with their difference operators or shifts

Xiao-Min Li and Hong-Xun Yi

University of Eastern Finland, Shandong University

Abstract

We prove a uniqueness theorem of nonconstant meromorphic functions sharing three distinct values IM and a fourth value CM with their shifts, and prove a uniqueness theorem of nonconstant entire functions sharing two distinct small functions IM with their shifts, which respectively improve Corollary 3.3(a) and Corollary 2.2(a) from \cite{12}, where the meromorphic functions and the entire functions are of hyper order less than $1.$ An example is provided to show that the above results are the best possible. We also prove two uniqueness theorems of nonconstant meromorphic functions sharing four distinct values with their difference operators.

Keywords: entire functions, meromorphic functions, shift sharing values, difference operators, uniqueness theorems

MSC numbers: 30D35, 30D30