This research concentrates on the analysis of meromorphic mappings. We derived several important results for value distribution of specific difference polynomials of meromorphic mappings, which generalize the work of Laine and Yang. In addition, we proved uniqueness theorems of meromorphic mappings. The difference polynomials of these functions have the same fixed points or share a nonzero valu...

In this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. We give some sufficient conditions for functions belonging to this class.

In this paper, we show that if two non-constant meromorphic functions f and g satisfy E(aj , k, f) = E(aj , k, g) for j = 1, 2, . . . , 5, where aj are five distinct small functions with respect to f and g, and k is a positive integer or ∞ with k ≥ 14, then f ≡ g. As a special case this also answers the longstanding problem on uniqueness of meromorphic functions concerning small functions.

In the paper we consider the problem of uniqueness of derivatives of meromorphic functions when they share two or three sets and obtained five results which will improve all the existing results. Key word and phrases: Meromorphic functions, uniqueness, weighted sharing, derivative, shared set.

where I is a finite set of distinct tuples (α0,α1, . . . ,αk) for which eachαi is a nonnegative integer, and the aᾱ are meromorphic functions in D = {z | |z| < 1}. For some index sets I, we determine conditions on aᾱ, whereby a meromorphic solution f of (1.1) in D will have finite order of growth as measured by the Ahlfors-Shimizu characteristic function. In [1], Bank investigated (1.1) where I...

The main purpose of this paper is to introduce and investigate a certain subclass of meromorphic close-to-convex functions. Such results as coefficient inequalities, convolution property, inclusion relationship, distortion property, and radius of meromorphic convexity are derived.

In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.