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Book Part Approximation of Discontinuous Functions by q-bernstein Polynomials(Springer international Publishing Ag, 2016) Ostrovska, Sofia; Ozban, Ahmet YasarThis chapter presents an overview of the results related to the q-Bernstein polynomials with q > 1 attached to discontinuous functions on [0, 1]. It is emphasized that the singularities of such functions located on the set Jq : = {0} boolean OR {q-l}(l=0, infinity), q > 1 are definitive for the investigation of the convergence properties of their q-Bernstein polynomials.
