Value distribution and uniqueness for q-difference of meromorphic functions Sharing Two Sets

TL;DR

This paper studies the value distribution and uniqueness of zero order transcendental meromorphic functions under q-difference operators, improving existing results and exploring set sharing with finite weight.

Contribution

It advances the understanding of value distribution for q-difference polynomials and establishes new uniqueness results for meromorphic functions sharing sets with their q-difference.

Findings

Improved bounds for value distribution of q-difference polynomials.

New uniqueness theorems for meromorphic functions sharing sets.

Examples illustrating the theoretical results.

Abstract

In this paper, we investigate the value distribution for linear q-difference polynomials of transcendental meromorphic functions of zero order which improves the results of Xu, Liu and Cao (\cite{Xu & Liu & Cao & 2015}). We also investigate the uniqueness of zero order meromorphic function with its q-difference operator sharing two sets with finite weight. Some examples have been exhibited which are relevant to the content of the paper.