Shape preserving properties of $ (\mathfrak{p}, \mathfrak{q}) $ Bernstein Bèzier curves and corresponding results over $ [a,b] $.

This article deals with shape preserving and local approximation properties of post-quantum Bernstein bases and operators over arbitrary interval $ [a, b] $ defined by Khan and Sharma (Iran J Sci Technol Trans Sci (2021)). The properties for $ (\mathfrak{p}, \mathfrak{q}) $-Bernstein bases and Bézier curves over $ [a, b] $ have been given. A de Casteljau algorithm has been discussed. Further we obtain the rate of convergence for $ (\mathfrak{p}, \mathfrak{q}) $-Bernstein operators over $ [a, b] $ in terms of Lipschitz type space having two parameters and Lipschitz maximal functions. [ABSTRACT FROM AUTHOR]