On King type modification of (p, q)-Lupa,sBernstein operators with improved estimates

This paper aims to modify the (p , q)-Lupa,s 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)-Lupas, Bernstein operators. King type modification of operators also provide better error estimation within some subinterval of [0, 1] in comparison to (p , q)-Lupa,s Bernstein operators. In the last section, some graphs and tables provided for simulation purposes using MATLAB (R2015a).

Automated summary

This paper aims to modify the (p, q)-Lupa's Bernstein operators using King's technique and establish the convergence results of these operators using the modulus of continuity and Lipschitz class functions. The paper obtains some approximation results for this new sequence of operators. It is shown that the King type modification of operators has a better convergence rate and provides better error estimation within some subinterval of [0, 1] compared to the (p, q)-Lupa's Bernstein operators. In the last section, some graphs and tables are provided for simulation purposes using MATLAB (R2015a).