Entire functions and their high order difference operators - Majumder, S.; Sarkar, N.; Pramanik, D. (Հայաստանի ԳԱԱ)
In this paper, we prove that for a transcendental entire function f of finite order such that λ(f − a) < ρ(f), where a is an entire function and satisfies ρ(a) < ρ(f), n ∈ N, if Δnc f and f share the entire function b satisfying ρ(b) < ρ(f) CM, where c ∈ C satisfies Δnc f ̸≡ 0, then f(z) = a(z)+decz, where d, c are two non-zero constants. In particular, if a = b, then a reduces to a constant. This result improves and generalizes the recent results of Chen and Chen [3], Liao and Zhang [10] and Lü et al. [11] in a large scale. Also we exhibit some relevant examples to fortify our results.
Keywords: Mathematics