Entire Functions Sharing Polynomial With Their Higher Order Derivative

It is shown that if f be a nonconstant entire function such that the hyper order \sigma_2(f)<\frac12 ,~k being a positive integer,~and if f and f^(k) share polynomial p(z) CM,~where p(z)=a_mz^m+a_m-1z^m-1+\cdots+a_0 with a_m\neq 0,~a_m-1,~\ldots,~a_0 are all constants,~then f^(k)(z)-p(z)=c(f(z)-p(z)) where c is a nonzero constant.