Value distribution of meromorphic functions concerning types of differential-difference polynomials sharing certain value CM and IM

The primary objective of this paper is to investigate the uniqueness of meromorphic functions that share specific values counting multiplicities (CM) and ignoring multiplicities (IM) in relation to differential-difference polynomials. This line of research originates from the polynomial introduced by Lin and Yi (Indian J. Pure Appl. Math., 35(2):121–132, 2004). Building on this, Pulak Sahoo and Biswajit Saha (Vietnam Journal of Mathematics, 44:531–540, 2016) established two results concerning differential polynomials that share certain values or fixed points, counting multiplicities. In this paper, we extend and improve upon some earlier findings, including the recent results by Pulak Sahoo and Biswajit Saha. To support our main results, we also provide several illustrative examples.