Department of Mathematics
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Browsing Department of Mathematics by Author "Almesbahi, Manal Mastafa"
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Item ON PROPERTIES OF q−BERNSTEIN POLYNOMIALS(2017-04-04) Almesbahi, Manal Mastafa; Turan, Mehmet; Ostrovska, SofiyaThe aim of this thesis is to study the theory of the Bernstein polynomials and its recent extension to the q-calculus. The main focus of the present study is on the q-Bernstein polynomials which appeared twenty years ago and have been attracting many researchers afterward. This work exhibits a review of well-known results on the Bernstein polynomials along with the necessary preliminaries, introduction to the the ory of the q-Bernstein polynomials, and some new developments. The latter include the result on strong operator limit for the sequence of the limit q-Bernstein operators and the proposition that the q-Bernstein operators are weakly Picard.