Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 2026 06 29 Uniqueness results on certain polynomials of meromorphic functions sharing a small function 10763 10.22075/ijnaa.2025.36923.5405 EN Harina P Waghamore Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056, India Naveenkumar B. N. Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056, India Journal Article 2025 02 17 This study explores specific polynomials that share a small function by applying the notions of weakly weighted and relaxed weighted sharing of meromorphic functions. In particular, the research delves into the uniqueness of two polynomial types related to the meromorphic function $f$: the homogeneous differential polynomial $\Phi[z]$ and the non-constant differential-difference polynomial $\Psi[z, f]$ and examines the value distribution of these polynomial functions within the context of weakly weighted and relaxed weighted sharing, resulting in the equation $\Phi[z] \equiv \Psi[z, f]$ (or) $\Phi[z]. \Psi[z, f] \equiv a^2$. The findings of this investigation enhance and extend the previous work of Harina P. Waghamore and Vijayalakshmi S. B. [27]. https://ijnaa.semnan.ac.ir/article_10763_21780a686b0ad3b45a6929f284dfd571.pdf