Abstract
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 by exploiting fractal approximation theory and considering the classical q-Bernstein polynomials as base functions, we construct a sequence of -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 of -fractal functions towards f follows from the convergence of the sequence of q-Bernstein polynomials of f towards f. If we consider a sequence of positive functions on a compact real interval that converges uniformly to a function f, we develop a double sequence of -fractal functions that converges uniformly to f.
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