Generalization of Value Distribution and Uniqueness of Certain Types of Difference Polynomials

Abstract

In this paper, we study the distribution of zeros and uniqueness of differential polynomials of the form fⁿ(z)(f(z)−1)^m ‖^d_j=1 f(z+c_j)^sj and fⁿ(z)(f^m(z)−1) ‖^d_j=1 f(z+c_j)^vj where c_j(j = 1,2,··· ,d) are complex constants, v_j(j = 1,2,··· ,d) are non-negative integers and σ = ∑^d_j=1 v_j sharing a small function with finite weight. The result obtained improves and generalizes the recent result.

Key words and phrases. Value distribution, Difference Polynomials, Fixed points, Sharing value.

1991 Mathematics Subject Classification. 30D35