Uniqueness of differential polynomial of meromorphic function with its q-shift
In the paper, we apply the concept of weighted sharing to study the uniqueness problems of differential polynomial of meromorphic function of zero order with its q-shift. The results of the paper improve and extend some recent results due to H. P. Waghamore and M. M. Manakame [Int. J. Open Problems Compt. Math., 18 (2025), 22-34]. A typical theorem obtained in the paper is as follows: Let P be a polynomial, f(z) be a non-constant meromorphic function of zero-order. Suppose that q is a non-zero complex constant, η C and n is an integer satisfying n≥ m+3τ+3Ω +6, where m=P, τ =_j=1^sμ _j and Ω =_j=1^sjμ _j. If f^n(z)P(f(z))_j=1^sf^(j)(z)^μ _j and f^n(qz+η )P(f(qz+η ))_j=1^sf^(j)(qz+η )^μ _j share (1,2) and (∞,∞), then f^n(z)P(f(z))_j=1^sf^(j)(z)^μ _j f^n(qz+η )P(f(qz+η ))_j=1^sf^(j)(qz+η )^μ _j . Three other similar theorems are also obtained in the paper. , number=1, journal=Matematychni Studii, author=Gurudas, Biswas, year=2025, month=Sep., pages=23-31