Unicity theorems for meromorphic functions sharing four small functions

Abstract

Let f and g be transcendental meromorphic functions in the complex plane having properties \bar{N}(r, f)≤uT(r, f)+S(r, f) and \bar{N}(r, g)≤vT(r, g)+S(r, g) for some constants u and v satisfying (u, v)∈[0, 1/19)×[0, 1/19). If there exist four distinct small meromorphic functions shared by f and g, then f=g.