Approximation properties and error estimation of q-Bernstein shifted operators

Abstract

In the present paper, q-analogue of Lupas Bernstein operators with shifted knots are introduced. First, some basic results for convergence of the introduced operators are established and then the rate of convergence by these operators in terms of the modulus of continuity are obtained. Further, a Voronovskaja type theorem and local approximation results for the said operators are studied. Error estimation tables are presented with respect to different parameters. We also show comparisons by some illustrative graphics for the convergence of operators to a function with the help of MATLAB R2018a.