| 초록 |
The continuous analysis, such as smoothness and uniform convergence, for polynomials and polynomial-like functions using differential operators have been studied considerably, parallel to the study of discrete analysis for these functions, using difference operators. In this work, for the difference operator ${ nabla}_h$ with size h gt; 0, we verify that for an integer $m{ geq}0$ and a strictly decreasing sequence $h_n$ converging to zero, a continuous function f(x) satisfying $${ nabla}_{h_n}^{m+1}f(kh_n)=0, text{ for every }n{ geq}1 text{ and }k{ in}{ mathbb{Z}}$$ , turns to be a polynomial of degree ${ leq}m$ . The proof used the polynomial convergence, and additionally, we investigated several conditions on convergence to polynomials. |
