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The quantum analogue of Bernstein operators $${\mathcal {B}}_{m,q}$$ reproduce the linear polynomials which are therefore eigenfunctions corresponding to the eigenvalue $$1,~\forall ~ q>0$$ . In this article the rest of… Click to show full abstract
The quantum analogue of Bernstein operators $${\mathcal {B}}_{m,q}$$ reproduce the linear polynomials which are therefore eigenfunctions corresponding to the eigenvalue $$1,~\forall ~ q>0$$ . In this article the rest of eigenstructure of q-Bernstein operators and the distinct behaviour of zeros of eigenfunctions for cases (i) $$1>q>0$$ , and (ii) $$q>1$$ are discussed. Graphical analysis for some eigenfunctions and their roots are presented with the help of MATLAB. Also, matrix representation for diagonalisation of q-Bernstein operators is discussed.
Journal Title: Analysis and Mathematical Physics
Year Published: 2020
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