Abstract

In this paper, by using the difference analogue of Nevanlinna's theory, the authors study the shared-value problem concerning two higher order difference operators of a transcendental entire function with finite order. The following conclusion is proved: Let f(z) be a finite order transcendental entire function such that &#x03BB;(f - a(z)) < &#x03C1;(f), where a(z)(&#x2208; S(f)) is an entire function and satisfies &#x03C1;(a(z)) < 1, and let &#x1D702;(&#x2208; &#x2102;) be a constant such that &#x2206;_&#x1D702;ⁿ⁺¹ f(z) &#x2262; 0. If &#x2206;_&#x1D702;ⁿ⁺¹ f(z) and &#x2206;_&#x1D702;ⁿ f(z) share &#x2206;_&#x1D702;ⁿ a(z) CM, where &#x2206;_&#x1D702;ⁿ a(z) &#x2208; S &#x2206;_&#x1D702;ⁿ⁺¹ f(z), then f(z) has a specific expression f(z) = a(z) + Be^Az, where A and B are two non-zero constants and a(z) reduces to a constant.