ENTIRE FUNCTIONS AND THEIR HIGHER ORDER DIFFERENCES

In this paper, we prove that for a transcendental entire function f(z) of finite order such that lambda(f - a(z)) < sigma(f), where a(z) is an entire function and satisfies sigma(a(z)) < 1, n is a positive integer, if Delta(n)(n) f(z) and f(z) share entire function b(z) (b(z) not equivalent to a(z)) satisfying sigma(b(z)) < 1 CM, where eta(is an element of C) satisfies Delta(n)(n) f(z) not equivalent to 0, then f(z) = a(z) + ce(c1 z), where c, c(1) are two nonzero constants.