Unicity of Meromorphic Functions Concerning Differential-Difference Polynomials

In this paper, we study unicity of meromorphic functions concerning differentialdifference polynomials and mainly prove: Let k(1), k(2), center dot center dot center dot, k(n) be nonnegative integers and k = max{k(1), k(2), center dot center dot center dot, k(n)}, let l be the number of distinct values of {0, c(1), c(2), center dot center dot center dot, c(n)}, let s be the number of distinct values of {c(1), c(2), center dot center dot center dot, c(n)}, let f(z) be a nonconstant meromorphic function of finite order satisfying N(r, f) <= 1/8(lk+l+2s-1)+1 T(r, f), let m(1)(z), m(2)(z), center dot center dot center dot, m(n)(z), a(z), b(z) be small functions of f(z) such that a(z) not equivalent to b(z), let (c(1), k(1)), (c(2), k(2)), center dot center dot center dot, (c(n), k(n)) be distinct and let F(z) = m(1)(z)f((k1))(z + c(1)) + m(2)(z)f((k2))(z + c(2)) + center dot center dot center dot + m(n)(z)f((kn))(z + c(n)). If f(z) and F(z) share a(z), b(z) CM, then f(z) equivalent to F(z). Our results improve and extend some results due to [1, 18, 20].