* Correspondence: [email protected]. com School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China Full list of author information is available at the end of the article Abstract In this article, we investigate the uniqueness problems of difference operators of two meromorphic functions. Uniqueness of a meromorphic function f and its difference operator with the ...

Abstract. The purpose of the present paper is to introduce new classMB(α, λ, q, s, A,B) of meromorphic functions defined by using a meromorphic analogue of the Choi-Saigo-Srivastava operator for the generalized hypergeometric function and investigate a number of inclusion relationships and radius problem of this class.The subordination relations, distortion theorems, and inequality properties a...

In this paper, we investigate the growth of solutions of the linear differential equation 0 = Bf f A f      , where ) (z A and 0) )( (  z B are meromorphic functions. More specifically, we estimate the lower bounded of hyperorder of solutions of the equation with respect to the conditions of ) (z A and 0) )( (  z B if solutions 0 ( f ) of the equation is of infinite order. keywords: ...

We show that if f is a transcendental meromorphic function with a finite number of poles and f has a cycle of Baker domains of period p, then there exist C > 1 and r0 > 0 such { z : 1 C r < |z| < Cr } sing(f−p) ∅, for r r0. We also give examples to show that this result fails for transcendental meromorphic functions with infinitely many poles.

In this paper, we introduce new classes, MBk(α, λ, q, s, ρ) and MTk(α, λ, q, s, ρ) of meromorphic functions defined by using a meromorphic analougue of the Choi-Saigo-Srivastava operator for the generalized hypergeometric function and investigate a number of inclusion relationships of these classes. We also derive some interesting properties of these classes, which also includes radius problem ...

Abstract. In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider th...

This paper deals with some uniqueness problems of meromorphic functions concerning their differential polynomials sharing the fixed-points or a small function with finite weight. These results in this paper greatly improve the recent results given by X.-Y. Zhang& J.-F. Chen and W.C. Lin[X.-Y. Zhang, J.-F. Chen, W.C. Lin , Entire or meromorphic functions sharing one value, Comput. Math. Appl. 56...

We show that there exists a function f meromorphic in the plane C such that the family of all functions g holomorphic in the unit disk D for which f ◦ g has no fixed point in D is not normal. This answers a question of Hinchliffe who had shown that this family is normal if Ĉ\f(C) does not consist of exactly one point in D. We also investigate the normality of the family of all holomorphic funct...

We shall assume that reader is familiar with the fundamental results and the standard notations of the Nevanlinna value distribution theory of meromorphic functions(see [11,14]). In addition, we will use the notation σ(f) to denote the order of growth of entire function f(z), σ2(f) to denote the hyper-order of f(z), λ(f)(λ2(f)) to denote the exponent(hyper-exponent) of convergence of the zero-s...

In this article, we obtain two results on $n$ the power of a meromorphic function and its shift operator sharing small together with value which improve complement some earlier results. particular, more or less have improved extended Qi-Yang [Meromorphic functions that share values their shifts $n$-th order differences, Analysis Math., 46(4)2020, 843-865] by dispelling superfluous conclusions i...