Fractal approximation is a well studied concept, but the convergence of all the existing fractal approximants towards the original function follows usually if the magnitude of the corresponding scaling factors approaches zero. In this article, for a given function $f\in \mathcal{C}(I),$ by exploiting fractal approximation theory and considering the classical q-Bernstein polynomials as base functions, we construct a sequence $\{f_n^{(q,\alpha )}(x){\}}_{n=1}^{\mathrm{\infty }}$ of $(q,\alpha )$-fractal functions that converges uniformly to f even if the norm/magnitude of the scaling functions/scaling factors does not tend to zero. The convergence of the sequence $\{f_n^{(q,\alpha )}(x){\}}_{n=1}^{\mathrm{\infty }}$ of $(q,\alpha )$-fractal functions towards f follows from the convergence of the sequence of q-Bernstein polynomials of f towards f. If we consider a sequence $\{f_m(x){\}}_{m=1}^{\mathrm{\infty }}$ of positive functions on a compact real interval that converges uniformly to a function f, we develop a double sequence $\{\{f_{m,n}^{(q,\alpha )}(x){\}}_{n=1}^{\mathrm{\infty }}{\}}_{m=1}^{\mathrm{\infty }}$ of $(q,\alpha )$-fractal functions that converges uniformly to f.

分形逼近是一个经过充分研究的概念，但是如果相应比例因子的大小接近零，则所有现有分形逼近通常会向原始函数收敛。在本文中，对于给定的函数$F\in \mathcal{C}(\mathrm{一世}),$利用分形逼近理论，以经典的q- Bernstein多项式为基函数，我们构造了一个序列。$\{F_n^{(q,\alpha )}(X){\}}_{n=1}^{\mathrm{\infty }}$ 的 $(q,\alpha )$-即使缩放函数/缩放因子的范数/大小不趋向于零，也均匀收敛到f的分形函数。序列的收敛$\{F_n^{(q,\alpha )}(X){\}}_{n=1}^{\mathrm{\infty }}$ 的 $(q,\alpha )$对f 的 -分形函数遵循f对f的q -Bernstein 多项式序列的收敛。如果我们考虑一个序列$\{F_{米}(X){\}}_{米=1}^{\mathrm{\infty }}$一致收敛于函数f的紧凑实数区间上的正函数，我们开发了一个双序列$\{\{F_{米,n}^{(q,\alpha )}(X){\}}_{n=1}^{\mathrm{\infty }}{\}}_{米=1}^{\mathrm{\infty }}$ 的 $(q,\alpha )$- 分形函数均匀收敛到f。