UNIQUENESS OF SOME DELAY-DIFFERENTIAL POLYNOMIALS SHARING A SMALL FUNCTION WITH FINITE WEIGHTS

. In this paper, we study the uniqueness problems of f n ( z ) L ( g ) and g n ( z ) L ( f ) when they share a non -zero small function alpha ( z ) with finite weights, where L ( h ) represents any one of h (k) ( z ) , h ( z + c ) , h ( z + c ) - h ( z ) and h (k) ( z + c ) , k >= 1 and c is a non -zero constant. Here f ( z ) and g ( z ) are transcendental meromorphic (or entire) functions and alpha ( z ) is a small function with respect to both f ( z ) and g ( z ) . Our results improve and supplement the recent results due to Gao and Liu [Bull. Korean Math. Soc. 59 (2022), 155-166].