Uniqueness of a meromorphic function and its linear difference polynomial sharing two sets with finite weight

TL;DR

This paper studies the uniqueness of meromorphic functions and their linear difference polynomials when sharing two sets with finite weight, improving previous results by reducing set sizes and weights.

Contribution

It introduces an improved uniqueness theorem for meromorphic functions sharing sets with their difference polynomials, refining earlier bounds on set cardinalities and weights.

Findings

Reduced the cardinality of the main set S

Lowered the weights associated with sharing sets

Provided examples validating the main results

Abstract

In this paper, we investigate the uniqueness property of meromorphic functions together with its linear difference polynomial sharing two sets. Using the polynomial introduced in [FILOMAT 33(18)(2019), 6055-6072], we have improved the result of Li-Chen [Abstract and Applied Analysis, 2014, Article ID 894968] in sense of reducing cardinalities of the main set S and the associated weights. Some examples have been exhibited to validate our certain claims in the main result.