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DAVID SWANSON, APPROXIMATION BY HÖLDER CONTINUOUS FUNCTIONS IN A SOBOLEV SPACE, The Rocky Mountain Journal of Mathematics, Vol. 44, No. 3 (2014), pp. 1027-1035 ...
Liu Wen, A Nowhere Differentiable Continuous Function Constructed Using Cantor Series, Mathematics Magazine, Vol. 74, No. 5 (Dec., 2001), pp. 400-402 ...
Technical Terms Bernstein polynomials: Polynomial functions that serve as building blocks for approximating continuous functions on closed intervals.