On limiting directions of entire solutions of complex differential-difference equations

In this article, we mainly obtain the measure of Julia limiting directions and transcendental directions of Jackson difference operators of non-trivial transcendental entire solutions for differential-difference equation f n ( z ) + ∑ k = 0 n a λ k ( z ) p λ k ( z , f ) = h ( z ) , where p λ k ( z , f ) ( λ ∈ ℕ ) are distinct differential-difference monomials, a λ k ( z ) are entire functions of growth smaller than that of the transcendental entire h ( z ). For non-trivial entire solutions f of differential-difference equation P 2 ( z , f ) + A 1 ( z ) P 1 ( z , f ) + A 0 ( z ) = 0 , where P λ ( z,f )(λ = 1, 2) are differential-difference polynomials. By considering the entire coefficient associated with Petrenko’s deviation, the measure of common transcendental directions of classical difference operators and Jackson difference operators of f was studied.