On King type modification of $(p,q)$-Lupaş Bernstein operators with improved estimates

Abstract

This paper aims to modify the $(p,q)$-Lupaş Bernstein operators using King's technique and to establish convergence results of these operators by using of modulus of continuity and Lipschitz class functions. Some approximation results for this new sequence of operators are obtained. It has been shown that the convergence rate of King type modification is better than the $(p,q)$-Lupaş Bernstein operators. King type modification of operators also provide better error estimation within some subinterval of $[0,1]$ in comparison to $(p,q)$-Lupaş Bernstein operators. In the last section, some graphs and tables provided for simulation purposes using MATLAB (R2015a).

Keywords

• post-quantum calculus
• $(p,q)$-lupaş bernstein operator
• modulus of continuity
• king type approximation
• error estimate