* Correspondence: [email protected]; [email protected] School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou 510006, China Full list of author information is available at the end of the article Abstract In the article, we study the normality of families of meromorphic ...

In the present investigation, the authors derive necessary and sufficient conditions for spirallikeness and convex spirallikeness of a suitably normalized meromorphic p-valent function in the punctured unit disk, using convolution. Also we give an application of our result to obtain a convolution condition for a class of meromorphic functions defined by a linear operator.

In this paper we introduce new subclasses of p-valent starlike, pvalent convex, p-valent close-to-convex and p-valent quasi-convex meromorphic functions and investigate some inclusion properties of these subclasses and investigate various inclusion properties and integral-preserving properties for the p-valent meromorphic function classes.

The purpose of the present paper is to establish some results concerning the partial sums of meromorphic starlike and meromorphic convex functions analogous to the results due to H. Silverman [J. Math. Anal. Appl. 209 (1997), 221-227]. Furthermore, we consider the partial sums of certain integral operator.

In this paper, we establish some results concerning the Hadamard product of certain meromorphic p-valent starlike and meromorphic p-valent convex functions analogous to those obtained by Vinod Kumar (J. Math. Anal. Appl. 113(1986), 230-234) and M. L. Mogra (Tamkang J. Math. 25(1994), no. 2, 157-162).

Among the invariant factors g of a positive semidefinite analytic function f on R, those g whose zero set Y is a curve are called special. We show that if each special g is a sum of squares of global meromorphic functions on a neighbourhood of Y , then f is a sum of squares of global meromorphic functions. Here sums can be (convergent) infinite, but we also find some sufficient conditions to ge...

We study the normality of families of meromorphic functions related to a result of Drasin. We consider whether a family meromorphic functions F whose each function does not take zero is normal in D, if for every pair of functions f and g in F, f z and g z share ∞ or H f − 1 and H g − 1 share 0, whereH f : f k z ak−1f k−1 z · · · , a0f z . Some examples show that the conditions in our results ar...

We study vanishing cycles of meromorphic functions. This gives a new and unitary point of view, extending the study of the topology of holomorphic germs – as initiated by Milnor in the sixties – and of the global topology of polynomial functions, which has been advanced more recently. We define singularities along the poles with respect to a certain (weak) stratification and prove local and glo...

Dealing with a question initiated by Liu [Meromorphic functions sharing set applications to difference equations, J. Math. Anal. Appl., 2009], we have investigated the situation when finite order entire function and its shift differential operator share two sets of small functions. Our result has improved extended results Chen-Chen [Entire their operators or shifts, Slovaca, 2013] Cui-Chen [The...