UNIQUENESS RELATED TO HIGHER ORDER DIFFERENCE OPERATORS OF ENTIRE FUNCTIONS

In this paper, by using the difference analogue of Nevanlinna's the-ory, the authors study the shared-value problem concerning two higher order dif-ference operators of a transcendental entire function with finite order. The follow-ing conclusion is proved: Let f(z) be a finite order transcendental entire function such that & lambda;(f - a(z)) < & rho;(f ), where a(z)(& ISIN; S(f)) is an entire function and satis-fies & rho;(a(z)) < 1, and let & eta;(& ISIN; C) be a constant such that & UDelta;n+1 & eta; f(z) & EQUIV;6 0. If & UDelta;n+1 & eta; f(z) and & UDelta;n & eta; f(z) share & UDelta;n & eta;a(z) CM, where & UDelta;n & eta;a(z) & ISIN; S �& UDelta;n+1 & eta; f (z)), then f(z) has a specific expression f(z) = a(z) + BeAz, where A and B are two non-zero constants and a(z) reduces to a constant.