In this paper, we define three subclasses Mp,αn,q(η,A,B),Ip,αn(λ,μ,γ),, Rpn,q(λ,μ,γ) connected with a q-analogue of linear differential operator Dα,p,Gn,q which consist functions F the form F(ζ)=ζ−p+∑j=1−p∞ajζj(p∈N) satisfying subordination condition p−1ηζDα,p,Gn,qF(ζ)′Dα,p,Gn,qF(ζ)+p≺p1+Aζ1+Bζ.Also, study various properties and characteristics subclass Mp,αn,q,∗(η,A,B) such as coefficients est...

the purpose of this article is to investigate the uniqueness of meromorphic functions sharing five small functions on annuli.

In this paper, we study the uniqueness problems on meromorphic function and its k th order derivative. The results in this paper improve the results given by K. W. Yu (On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4(1)(2003), Art. 21), L. P. Liu and Y. X. Gu (Uniqueness of meromorphic functions that share one small function w...

Let K be a non archimedean algebraically closed field of characteristic π, complete for its ultrametric absolute value. In a recent paper by Escassut and Yang ([6]) polynomial decompositions P (f) = Q(g) for meromorphic functions f , g on K (resp. in a disk d(0, r−) ⊂ K) have been considered, and for a class of polynomials P , Q, estimates for the Nevanlinna function T (ρ, f) have been derived....